The cephes Reference Manual

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The cephes Reference Manual

This is the cephes Reference Manual, version 1.2, generated automatically by Declt version 3.0 "Montgomery Scott" on Sun May 15 03:28:32 2022 GMT+0.


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1 Introduction

Cephes Mathematical Library

A common lisp CFFI wrapper for the SciPy version of Cephes special functions.

For many years Cephes was considered the gold standard in cross-platform mathematical libraries, superior to the libm distributions of the time (early 1990's). Since then C99 and later ANSI C specifications have closed the gap, but there are still certain special and statistical functions available in Cephes that are not in the standard C libraries.

The SciPy version differs from standard Cephes in that it has some additional functions, improvements in accuracy, and is better documented. Only double-float versions are provided.

Installation

The ASDF file will automatically build the shared library as part of the load operation. If you need to build on a system other than MS Windows or UNIX, you will need to modify the make file to account for the linker command to create a shared library.

As delivered, the Makefile is set-up to work on MS Windows or UNIX, and you can build it manually like so:

cd scipy-cephes && make

If you build this on another platform, please drop a note into a Cephes repository issue with the build instructions so we can update the Makefile and system definition.

The init.lisp file, where CFFI loads the library, should work out of the box if libmd on the path somewhere, regardless of platform. If in doubt, place a copy in the same directory as this README.

Documentation

If you know your way around special functions, the table below should suffice to get started. For a more complete description, see the doc strings in cephes.lisp. Finally, the C source code itself, referenced in cephes.lisp, is thorough and complete from a mathematical perspective.

You can also use the scipy.special online documentation.

The API

There is no overlap between the wrapped Cephes functions and the Common Lisp numerical tower. All functions are in the cephes package.

Exported functions are:

| function | description | |-------------------|-------------------------------------------------------------------------------| | airy | Airy function | | bdtr | Binomial distribution | | bdtrc | Complement of binomial distribution | | bdtri | Inverse binomial distribution | | besselpoly | Weighted integral of the Bessel function of the first kind | | beta | Beta function | | lbeta | Natural log of beta | | btdtr | incomplete beta integral | | cbrt | cube root | | chdtr | Chi-square distribution | | chdtrc | Complemented Chi-square distribution | | chdtri | Inverse of complemented Chi-square distribution | | dawsn | Dawson's Integral | | ellik | Incomplete elliptic integral of the first kind | | ellie | Incomplete elliptic integral of the second kind | | ellpk | Complete elliptic integral of the first kind | | ellpe | Complete elliptic integral of the second kind | | jacobian-elliptic | jacobian Elliptic Functions | | exp2 | Base 2 exponential function | | exp10 | Base 10 exponential function (Common antilogarithm) | | expn | Exponential integral | | fdtr | F distribution | | fdtrc | Complemented F distribution | | fdtri | Inverse of F distribution | | fresnl | Fresnel integral | | gamma | Gamma function | | log-gamma | Natural logarithm of Gamma function | | gdtr | Gamma distribution function | | gdtrc | Complemented Gamma distribution function | | gdtri | Inverse Gamma distribution function (?) - not documented in src | | hyp2f1 | Gauss hypergeometric function | | hyperg | Confluent hypergeometric function | | i0 | Modified Bessel function of order zero | | i0e | Modified Bessel function of order zero, exponentially scaled | | i1 | Modified Bessel function of order one | | i1e | Modified Bessel function of order one, exponentially scaled | | igam | Regularized lower incomplete gamma function | | igamc | Regularized upper incomplete gamma function | | igami | Inverse of the lower incomplete gamma function | | igamci | Inverse of the upper incomplete gamma function | | incbet | Incomplete beta integral | | incbi | Inverse of incomplete beta integral | | iv | Modified Bessel function of noninteger order | | j0 | Bessel function of order zero | | y0 | Bessel function of the second kind, order zero | | j1 | Bessel function of order one | | y1 | Bessel function of second kind of order one | | jv | Bessel function of noninteger order | | k0 | Modified Bessel function, third kind, order zero | | k0e | Modified Bessel function, third kind, order zero, exponentially scaled | | k1 | Modified Bessel function of the third kind of order one | | k1e | Modified Bessel function of the third kind of order one, exponentially scaled | | kn | Modified Bessel function, third kind, integer order | | nbdtr | Negative binomial distribution | | nbdtrc | Complemented negative binomial distribution | | nbdtri | Inverse complemented negative binomial distribution | | ndtr | Normal distribution function | | log-ndtr | Log of the normal distribution function | | erf | Error function | | erfc | Complementary error function | | erfinv | Inverse of the error function | | erfcinv | Inverse of the complementary error function | | ndtri | Inverse of Normal distribution function | | pdtr | Poisson distribution | | pdtrc | Complemented poisson distribution | | pdtri | Inverse Poisson distribution | | poch | Pochhammer symbol (a)_m = gamma(a + m) / gamma(a) | | psi | Psi (digamma) function | | rgamma | Reciprocal Gamma function | | shichi | Hyperbolic sine and cosine integrals | | sici | Sine and cosine integrals | | sindg | Circular sine of angle in degrees | | cosdg | Circular cosine of angle in degrees | | sinpi | Compute sin(pi * x) | | cospi | Compute cos(pi * x) | | spence | Dilogarithm | | stdtr | Student's t distribution | | stdtri | Functional inverse of Student's t distribution | | yv | Bessel function of noninteger order | | tandg | Circular tangent of angle in degrees | | cotdg | Circular cotangent of argument in degrees | | log1p | log(1 + x) | | log1pmx | log(1 + x) - x | | expm1 | exp(x) - 1 | | cosm1 | cos(x) - 1 | | lgam1p | lgam(x + 1) | | yn | Bessel function of second kind of integer order | | zeta | Riemann zeta function of two arguments | | zetac | Riemann zeta function | | owens-t | Owen's T-Function |

Contributing

When contributing to this repository, please first discuss major changes to the existing code you wish to make via a github issue. Minor changes and major additions are welcome. Please write good commit messages.

License

CEPHES.CL is available under the Microsoft Public License.


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2 Systems

The main system appears first, followed by any subsystem dependency.


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2.1 cephes

Author

Steven Nunez <steve@symbolics.tech>

License

MS-PL

Description

Wrapper for the Cephes Mathematical Library

Version

1.2

Dependency

cffi

Source

cephes.asd (file)

Components

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3 Modules

Modules are listed depth-first from the system components tree.


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3.1 cephes/libmd

Parent

cephes (system)

Location

/home/quickref/quicklisp/dists/quicklisp/software/cephes.cl-20211020-git/libmd/ (not found)

Component

makefile.m (file)


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4 Files

Files are sorted by type and then listed depth-first from the systems components trees.


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4.1 Lisp


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4.1.1 cephes.asd

Location

cephes.asd

Systems

cephes (system)


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4.1.2 cephes/package.lisp

Dependency

libmd (module)

Parent

cephes (system)

Location

package.lisp

Packages

cephes


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4.1.3 cephes/init.lisp

Dependency

package.lisp (file)

Parent

cephes (system)

Location

init.lisp


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4.1.4 cephes/cephes.lisp

Dependency

init.lisp (file)

Parent

cephes (system)

Location

cephes.lisp

Exported Definitions
Internal Definitions

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4.2 Other


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4.2.1 cephes/libmd/makefile.m

Parent

libmd (module)

Location

/home/quickref/quicklisp/dists/quicklisp/software/cephes.cl-20211020-git/libmd/makefile.m (not found)


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5 Packages

Packages are listed by definition order.


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5.1 cephes

Source

package.lisp (file)

Use List

common-lisp

Exported Definitions
Internal Definitions

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6 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.


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6.1 Exported definitions


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6.1.1 Functions

Function: airy X

Solution of the differential equation y”(x) = xy
The function returns the two independent solutions Ai, Bi and their first derivatives Ai’(x), Bi’(x), as VALUES (Ai Bi Aip Bip)

Package

cephes

Source

cephes.lisp (file)

Function: bdtr K N P

Returns the sum of the terms 0 through k of the Binomial probability density

Package

cephes

Source

cephes.lisp (file)

Function: bdtrc K N P

Returns the sum of the terms k+1 through n of the Binomial probability density

Package

cephes

Source

cephes.lisp (file)

Function: bdtri K N Y

Finds the event probability p such that the sum of the terms 0 through k of the Binomial probability densityis equal to the given cumulative probability y.

Package

cephes

Source

cephes.lisp (file)

Function: besselpoly A LAMBDA NU
Package

cephes

Source

cephes.lisp (file)

Function: beta A B
Package

cephes

Source

cephes.lisp (file)

Function: btdtr A B X

Returns the area from zero to x under the beta density function.

x
- -
| (a+b) | | a-1 b-1
P(x) = ———- | t (1-t) dt
- - | |
| (a) | (b) -
0

This function is identical to the incomplete beta integral function incbet(a, b, x).

Package

cephes

Source

cephes.lisp (file)

Function: cbrt X

Returns the cube root of the argument, which may be negative.

Package

cephes

Source

cephes.lisp (file)

Function: chdtr DF X

Returns the area under the left hand tail (from 0 to x) of the Chi square probability density function with DF degrees of freedom.

Package

cephes

Source

cephes.lisp (file)

Function: chdtrc DF X

Returns the area under the right hand tail (from x to infinity) of the Chi square probability density function with DF degrees of freedom

Package

cephes

Source

cephes.lisp (file)

Function: chdtri DF Y

Finds the Chi-square argument x such that the integral from x to infinity of the Chi-square density is equal to the given cumulative probability y

Package

cephes

Source

cephes.lisp (file)

Function: cosdg D M S

Range reduction is into intervals of 45 degrees.

Package

cephes

Source

cephes.lisp (file)

Function: cosm1 X
Package

cephes

Source

cephes.lisp (file)

Function: cospi X
Package

cephes

Source

cephes.lisp (file)

Function: cotdg X

Returns the circular cotangent of the argument x in degrees

Package

cephes

Source

cephes.lisp (file)

Function: dawsn XX
Package

cephes

Source

cephes.lisp (file)

Function: ellie PHI M
Package

cephes

Source

cephes.lisp (file)

Function: ellik PHI M
Package

cephes

Source

cephes.lisp (file)

Function: ellpe X
Package

cephes

Source

cephes.lisp (file)

Function: ellpk X
Package

cephes

Source

cephes.lisp (file)

Function: erf X
Package

cephes

Source

cephes.lisp (file)

Function: erfc A
Package

cephes

Source

cephes.lisp (file)

Function: erfcinv Y

Computes the inverse of the complimentary error function on the restricted domain 0 < y < 2. This restriction ensures the existence of a unique result such that erfc(erfcinv(y)) = y.

Package

cephes

Source

cephes.lisp (file)

Function: erfinv Y

Inverse of the error function.
Computes the inverse of the error function on the restricted domain -1 < y < 1. This restriction ensures the existence of a unique result such that erf(erfinv(y)) = y.

Package

cephes

Source

cephes.lisp (file)

Function: exp10 X

Returns 10 raised to the x power.

Package

cephes

Source

cephes.lisp (file)

Function: exp2 X

Returns 2 raised to the x power.

Package

cephes

Source

cephes.lisp (file)

Function: expm1 X
Package

cephes

Source

cephes.lisp (file)

Function: expn N X

Evaluates the exponential integral

Package

cephes

Source

cephes.lisp (file)

Function: fdtr A B X

Returns the area from zero to x under the F density function

Package

cephes

Source

cephes.lisp (file)

Function: fdtrc A B X

Returns the area from x to infinity under the F density function

Package

cephes

Source

cephes.lisp (file)

Function: fdtri A B Y

Finds the F density argument x such that the integral from -infinity to x of the F density is equal to the given probability p

Package

cephes

Source

cephes.lisp (file)

Function: fresnl XXA
Package

cephes

Source

cephes.lisp (file)

Function: gamma X

Returns Gamma function of the argument. The result is correctly signed.

Package

cephes

Source

cephes.lisp (file)

Function: gdtr A B X

Returns the integral from zero to x of the Gamma probability density function

Package

cephes

Source

cephes.lisp (file)

Function: gdtrc A B X

Returns the integral from x to infinity of the Gamma probability density function

Package

cephes

Source

cephes.lisp (file)

Function: gdtri A B Y
Package

cephes

Source

cephes.lisp (file)

Function: hyp2f1 A B C X
Package

cephes

Source

cephes.lisp (file)

Function: hyperg A B X

Computes the confluent hypergeometric function

Package

cephes

Source

cephes.lisp (file)

Function: i0 X

Returns modified Bessel function of order zero of the argument

Package

cephes

Source

cephes.lisp (file)

Function: i0e X

Returns exponentially scaled modified Bessel function of order zero of the argument

Package

cephes

Source

cephes.lisp (file)

Function: i1 X

Returns modified Bessel function of order one of the argument

Package

cephes

Source

cephes.lisp (file)

Function: i1e X

Returns exponentially scaled modified Bessel function of order one of the argument

Package

cephes

Source

cephes.lisp (file)

Function: igam A X
Package

cephes

Source

cephes.lisp (file)

Function: igamc A X
Package

cephes

Source

cephes.lisp (file)

Function: igamci A Q
Package

cephes

Source

cephes.lisp (file)

Function: igami A P

Returns the x such that: igamc(a, x) = p
The input argument a must be positive and p must be between 0 and 1.

Package

cephes

Source

cephes.lisp (file)

Function: incbet AA BB XX

Returns incomplete beta integral of the arguments, evaluated from zero to x.

Package

cephes

Source

cephes.lisp (file)

Function: incbi AA BB YY0

Given y, the function finds x such that incbet( a, b, x ) = y

Package

cephes

Source

cephes.lisp (file)

Function: iv V X

Returns modified Bessel function of order v of the argument. If x is negative, v must be integer valued.

Package

cephes

Source

cephes.lisp (file)

Function: j0 X

Returns Bessel function of order zero of the argument

Package

cephes

Source

cephes.lisp (file)

Function: j1 X

Returns Bessel function of order one of the argument.

Package

cephes

Source

cephes.lisp (file)

Function: jacobian-elliptic U M

Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m), and dn(u|m) of parameter m between 0 and 1, and real argument u. Returns VALUES (sn cn dn)

Package

cephes

Source

cephes.lisp (file)

Function: jv V X

Returns Bessel function of order v of the argument, where v is real. Negative x is allowed if v is an integer.

Package

cephes

Source

cephes.lisp (file)

Function: k0 X

Returns modified Bessel function of the third kind of order zero of the argument.

Package

cephes

Source

cephes.lisp (file)

Function: k0e X

Returns exponentially scaled modified Bessel function of the third kind of order zero of the argument.

Package

cephes

Source

cephes.lisp (file)

Function: k1 X

Computes the modified Bessel function of the third kind of order one of the argument.

Package

cephes

Source

cephes.lisp (file)

Function: k1e X

Returns exponentially scaled modified Bessel function of the third kind of order one of the argument

Package

cephes

Source

cephes.lisp (file)

Function: kn NN X

Returns modified Bessel function of the third kind of order n of the argument

Package

cephes

Source

cephes.lisp (file)

Function: lanczos-sum X
Package

cephes

Source

cephes.lisp (file)

Function: lanczos-sum-near-1 X
Package

cephes

Source

cephes.lisp (file)

Function: lanczos-sum-near-2 X
Package

cephes

Source

cephes.lisp (file)

Function: lanczos-sum-scaled X
Package

cephes

Source

cephes.lisp (file)

Function: lbeta A B
Package

cephes

Source

cephes.lisp (file)

Function: lgam1p X
Package

cephes

Source

cephes.lisp (file)

Function: log-gamma X

Returns the base e logarithm of the absolute value of the Gamma function of the argument.

Package

cephes

Source

cephes.lisp (file)

Function: log-ndtr A
Package

cephes

Source

cephes.lisp (file)

Function: log1p X
Package

cephes

Source

cephes.lisp (file)

Function: log1pmx X
Package

cephes

Source

cephes.lisp (file)

Function: nbdtr K N P

Returns the sum of the terms 0 through k of the negative binomial distribution

Package

cephes

Source

cephes.lisp (file)

Function: nbdtrc K N P

Returns the sum of the terms k+1 to infinity of the negative binomial distribution

Package

cephes

Source

cephes.lisp (file)

Function: nbdtri K N P

Returns the sum of the terms k+1 to infinity of the negative binomial distribution

Package

cephes

Source

cephes.lisp (file)

Function: ndtr A

Returns the area under the Gaussian probability density function, integrated from minus infinity to x

Package

cephes

Source

cephes.lisp (file)

Function: ndtri Y0

Returns the argument, x, for which the area under the Gaussian probability density function (integrated from minus infinity to x) is equal to y.
For small arguments 0 < y < exp(-2), the program computes z = sqrt( -2.0 * log(y) ); then the approximation is x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).

Package

cephes

Source

cephes.lisp (file)

Function: owens-t H A
Package

cephes

Source

cephes.lisp (file)

Function: pdtr K M

Returns the sum of the first k terms of the Poisson distribution

Package

cephes

Source

cephes.lisp (file)

Function: pdtrc K M

Returns the sum of the terms k+1 to infinity of the Poisson distribution

Package

cephes

Source

cephes.lisp (file)

Function: pdtri K Y

Finds the Poisson variable x such that the integral from 0 to x of the Poisson density is equal to the given probability y

Package

cephes

Source

cephes.lisp (file)

Function: poch X M
Package

cephes

Source

cephes.lisp (file)

Function: psi X

Returns the logarithmic derivative of the gamma function

Package

cephes

Source

cephes.lisp (file)

Function: rgamma X

Returns one divided by the Gamma function of the argument

Package

cephes

Source

cephes.lisp (file)

Function: shichi X

Returns VALUES (si ci)

Package

cephes

Source

cephes.lisp (file)

Function: sici X

Returns VALUES (si ci)

Package

cephes

Source

cephes.lisp (file)

Function: sindg D M S

Range reduction is into intervals of 45 degrees.

Package

cephes

Source

cephes.lisp (file)

Function: sinpi X
Package

cephes

Source

cephes.lisp (file)

Function: spence X
Package

cephes

Source

cephes.lisp (file)

Function: stdtr K T1

Computes the integral from minus infinity to t of the Student t distribution with integer k > 0 degrees of freedom

Package

cephes

Source

cephes.lisp (file)

Function: stdtri K P

Given probability p, finds the argument t such that stdtr(k,t) is equal to p

Package

cephes

Source

cephes.lisp (file)

Function: tandg X

Returns the circular tangent of the argument x in degrees

Package

cephes

Source

cephes.lisp (file)

Function: y0 X

Bessel function of the second kind, order zero

Package

cephes

Source

cephes.lisp (file)

Function: y1 X

Returns Bessel function of the second kind of order one of the argument.

Package

cephes

Source

cephes.lisp (file)

Function: yn N X

Returns Bessel function of order n, where n is a (possibly negative) integer

Package

cephes

Source

cephes.lisp (file)

Function: yv V X
Package

cephes

Source

cephes.lisp (file)

Function: zeta X Q
Package

cephes

Source

cephes.lisp (file)

Function: zetac X
Package

cephes

Source

cephes.lisp (file)


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6.2 Internal definitions


Previous: , Up: Internal definitions   [Contents][Index]

6.2.1 Functions

Function: cephes-airy X AI AIP BI BIP

Solution of the differential equation y”(x) = xy
The function returns the two independent solutions Ai, Bi and their first derivatives Ai’(x), Bi’(x).

Package

cephes

Source

cephes.lisp (file)

Function: cephes-ellpj U M SN CN DN PHI
Package

cephes

Source

cephes.lisp (file)

Function: cephes-fresnl XXA SSA CCA

Evaluates S and C fresnel integrals and returns VALUES (S C)

Package

cephes

Source

cephes.lisp (file)

Function: cephes-shichi X SI CI
Package

cephes

Source

cephes.lisp (file)

Function: cephes-sici X SI CI
Package

cephes

Source

cephes.lisp (file)

Function: sign-gamma X
Package

cephes

Source

cephes.lisp (file)


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Appendix A Indexes


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A.1 Concepts

Jump to:   C   F   L   M   O  
Index Entry  Section

C
cephes.asd: The cephes․asd file
cephes/cephes.lisp: The cephes/cephes․lisp file
cephes/init.lisp: The cephes/init․lisp file
cephes/libmd: The cephes/libmd module
cephes/libmd/makefile.m: The cephes/libmd/makefile․m file
cephes/package.lisp: The cephes/package․lisp file

F
File, Lisp, cephes.asd: The cephes․asd file
File, Lisp, cephes/cephes.lisp: The cephes/cephes․lisp file
File, Lisp, cephes/init.lisp: The cephes/init․lisp file
File, Lisp, cephes/package.lisp: The cephes/package․lisp file
File, other, cephes/libmd/makefile.m: The cephes/libmd/makefile․m file

L
Lisp File, cephes.asd: The cephes․asd file
Lisp File, cephes/cephes.lisp: The cephes/cephes․lisp file
Lisp File, cephes/init.lisp: The cephes/init․lisp file
Lisp File, cephes/package.lisp: The cephes/package․lisp file

M
Module, cephes/libmd: The cephes/libmd module

O
Other File, cephes/libmd/makefile.m: The cephes/libmd/makefile․m file

Jump to:   C   F   L   M   O  

Next: , Previous: , Up: Indexes   [Contents][Index]

A.2 Functions

Jump to:   A   B   C   D   E   F   G   H   I   J   K   L   N   O   P   R   S   T   Y   Z  
Index Entry  Section

A
airy: Exported functions

B
bdtr: Exported functions
bdtrc: Exported functions
bdtri: Exported functions
besselpoly: Exported functions
beta: Exported functions
btdtr: Exported functions

C
cbrt: Exported functions
cephes-airy: Internal functions
cephes-ellpj: Internal functions
cephes-fresnl: Internal functions
cephes-shichi: Internal functions
cephes-sici: Internal functions
chdtr: Exported functions
chdtrc: Exported functions
chdtri: Exported functions
cosdg: Exported functions
cosm1: Exported functions
cospi: Exported functions
cotdg: Exported functions

D
dawsn: Exported functions

E
ellie: Exported functions
ellik: Exported functions
ellpe: Exported functions
ellpk: Exported functions
erf: Exported functions
erfc: Exported functions
erfcinv: Exported functions
erfinv: Exported functions
exp10: Exported functions
exp2: Exported functions
expm1: Exported functions
expn: Exported functions

F
fdtr: Exported functions
fdtrc: Exported functions
fdtri: Exported functions
fresnl: Exported functions
Function, airy: Exported functions
Function, bdtr: Exported functions
Function, bdtrc: Exported functions
Function, bdtri: Exported functions
Function, besselpoly: Exported functions
Function, beta: Exported functions
Function, btdtr: Exported functions
Function, cbrt: Exported functions
Function, cephes-airy: Internal functions
Function, cephes-ellpj: Internal functions
Function, cephes-fresnl: Internal functions
Function, cephes-shichi: Internal functions
Function, cephes-sici: Internal functions
Function, chdtr: Exported functions
Function, chdtrc: Exported functions
Function, chdtri: Exported functions
Function, cosdg: Exported functions
Function, cosm1: Exported functions
Function, cospi: Exported functions
Function, cotdg: Exported functions
Function, dawsn: Exported functions
Function, ellie: Exported functions
Function, ellik: Exported functions
Function, ellpe: Exported functions
Function, ellpk: Exported functions
Function, erf: Exported functions
Function, erfc: Exported functions
Function, erfcinv: Exported functions
Function, erfinv: Exported functions
Function, exp10: Exported functions
Function, exp2: Exported functions
Function, expm1: Exported functions
Function, expn: Exported functions
Function, fdtr: Exported functions
Function, fdtrc: Exported functions
Function, fdtri: Exported functions
Function, fresnl: Exported functions
Function, gamma: Exported functions
Function, gdtr: Exported functions
Function, gdtrc: Exported functions
Function, gdtri: Exported functions
Function, hyp2f1: Exported functions
Function, hyperg: Exported functions
Function, i0: Exported functions
Function, i0e: Exported functions
Function, i1: Exported functions
Function, i1e: Exported functions
Function, igam: Exported functions
Function, igamc: Exported functions
Function, igamci: Exported functions
Function, igami: Exported functions
Function, incbet: Exported functions
Function, incbi: Exported functions
Function, iv: Exported functions
Function, j0: Exported functions
Function, j1: Exported functions
Function, jacobian-elliptic: Exported functions
Function, jv: Exported functions
Function, k0: Exported functions
Function, k0e: Exported functions
Function, k1: Exported functions
Function, k1e: Exported functions
Function, kn: Exported functions
Function, lanczos-sum: Exported functions
Function, lanczos-sum-near-1: Exported functions
Function, lanczos-sum-near-2: Exported functions
Function, lanczos-sum-scaled: Exported functions
Function, lbeta: Exported functions
Function, lgam1p: Exported functions
Function, log-gamma: Exported functions
Function, log-ndtr: Exported functions
Function, log1p: Exported functions
Function, log1pmx: Exported functions
Function, nbdtr: Exported functions
Function, nbdtrc: Exported functions
Function, nbdtri: Exported functions
Function, ndtr: Exported functions
Function, ndtri: Exported functions
Function, owens-t: Exported functions
Function, pdtr: Exported functions
Function, pdtrc: Exported functions
Function, pdtri: Exported functions
Function, poch: Exported functions
Function, psi: Exported functions
Function, rgamma: Exported functions
Function, shichi: Exported functions
Function, sici: Exported functions
Function, sign-gamma: Internal functions
Function, sindg: Exported functions
Function, sinpi: Exported functions
Function, spence: Exported functions
Function, stdtr: Exported functions
Function, stdtri: Exported functions
Function, tandg: Exported functions
Function, y0: Exported functions
Function, y1: Exported functions
Function, yn: Exported functions
Function, yv: Exported functions
Function, zeta: Exported functions
Function, zetac: Exported functions

G
gamma: Exported functions
gdtr: Exported functions
gdtrc: Exported functions
gdtri: Exported functions

H
hyp2f1: Exported functions
hyperg: Exported functions

I
i0: Exported functions
i0e: Exported functions
i1: Exported functions
i1e: Exported functions
igam: Exported functions
igamc: Exported functions
igamci: Exported functions
igami: Exported functions
incbet: Exported functions
incbi: Exported functions
iv: Exported functions

J
j0: Exported functions
j1: Exported functions
jacobian-elliptic: Exported functions
jv: Exported functions

K
k0: Exported functions
k0e: Exported functions
k1: Exported functions
k1e: Exported functions
kn: Exported functions

L
lanczos-sum: Exported functions
lanczos-sum-near-1: Exported functions
lanczos-sum-near-2: Exported functions
lanczos-sum-scaled: Exported functions
lbeta: Exported functions
lgam1p: Exported functions
log-gamma: Exported functions
log-ndtr: Exported functions
log1p: Exported functions
log1pmx: Exported functions

N
nbdtr: Exported functions
nbdtrc: Exported functions
nbdtri: Exported functions
ndtr: Exported functions
ndtri: Exported functions

O
owens-t: Exported functions

P
pdtr: Exported functions
pdtrc: Exported functions
pdtri: Exported functions
poch: Exported functions
psi: Exported functions

R
rgamma: Exported functions

S
shichi: Exported functions
sici: Exported functions
sign-gamma: Internal functions
sindg: Exported functions
sinpi: Exported functions
spence: Exported functions
stdtr: Exported functions
stdtri: Exported functions

T
tandg: Exported functions

Y
y0: Exported functions
y1: Exported functions
yn: Exported functions
yv: Exported functions

Z
zeta: Exported functions
zetac: Exported functions

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A.3 Variables


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A.4 Data types

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Index Entry  Section

C
cephes: The cephes system
cephes: The cephes package

P
Package, cephes: The cephes package

S
System, cephes: The cephes system

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