This is the cephes Reference Manual, version 1.4.0, generated automatically by Declt version 4.0 beta 2 "William Riker" on Sun Sep 15 03:34:34 2024 GMT+0.
The main system appears first, followed by any subsystem dependency.
cephesWrapper for the Cephes Mathematical Library
Steven Nunez <steve@symbolics.tech>
MS-PL
1.4.0
cffi (system).
libmd (module).
package.lisp (file).
init.lisp (file).
cephes.lisp (file).
Modules are listed depth-first from the system components tree.
Files are sorted by type and then listed depth-first from the systems components trees.
cephes/package.lispcephes/cephes.lispinit.lisp (file).
cephes (system).
airy (function).
bdtr (function).
bdtrc (function).
bdtri (function).
besselpoly (function).
beta (function).
btdtr (function).
cbrt (function).
chdtr (function).
chdtrc (function).
chdtri (function).
cosdg (function).
cosm1 (function).
cospi (function).
cotdg (function).
dawsn (function).
ellie (function).
ellik (function).
ellpe (function).
ellpk (function).
erf (function).
erfc (function).
erfcinv (function).
erfinv (function).
exp10 (function).
exp2 (function).
expm1 (function).
expn (function).
fdtr (function).
fdtrc (function).
fdtri (function).
fresnl (function).
gamma (function).
gdtr (function).
gdtrc (function).
gdtri (function).
hyp2f1 (function).
hyperg (function).
i0 (function).
i0e (function).
i1 (function).
i1e (function).
igam (function).
igamc (function).
igamci (function).
igami (function).
incbet (function).
incbi (function).
iv (function).
j0 (function).
j1 (function).
jacobian-elliptic (function).
jv (function).
k0 (function).
k0e (function).
k1 (function).
k1e (function).
kn (function).
lanczos-sum (function).
lanczos-sum-near-1 (function).
lanczos-sum-near-2 (function).
lanczos-sum-scaled (function).
lbeta (function).
lgam1p (function).
log-gamma (function).
log-ndtr (function).
log1p (function).
log1pmx (function).
nbdtr (function).
nbdtrc (function).
nbdtri (function).
ndtr (function).
ndtri (function).
owens-t (function).
pdtr (function).
pdtrc (function).
pdtri (function).
poch (function).
psi (function).
rgamma (function).
shichi (function).
sici (function).
sindg (function).
sinpi (function).
spence (function).
stdtr (function).
stdtri (function).
tandg (function).
y0 (function).
y1 (function).
yn (function).
yv (function).
zeta (function).
zetac (function).
cephes-airy (function).
cephes-ellpj (function).
cephes-fresnl (function).
cephes-shichi (function).
cephes-sici (function).
evlrat (function).
sign-gamma (function).
Packages are listed by definition order.
cephescommon-lisp.
airy (function).
bdtr (function).
bdtrc (function).
bdtri (function).
besselpoly (function).
beta (function).
btdtr (function).
cbrt (function).
chdtr (function).
chdtrc (function).
chdtri (function).
cosdg (function).
cosm1 (function).
cospi (function).
cotdg (function).
dawsn (function).
ellie (function).
ellik (function).
ellpe (function).
ellpk (function).
erf (function).
erfc (function).
erfcinv (function).
erfinv (function).
exp10 (function).
exp2 (function).
expm1 (function).
expn (function).
fdtr (function).
fdtrc (function).
fdtri (function).
fresnl (function).
gamma (function).
gdtr (function).
gdtrc (function).
gdtri (function).
hyp2f1 (function).
hyperg (function).
i0 (function).
i0e (function).
i1 (function).
i1e (function).
igam (function).
igamc (function).
igamci (function).
igami (function).
incbet (function).
incbi (function).
iv (function).
j0 (function).
j1 (function).
jacobian-elliptic (function).
jv (function).
k0 (function).
k0e (function).
k1 (function).
k1e (function).
kn (function).
lanczos-sum (function).
lanczos-sum-near-1 (function).
lanczos-sum-near-2 (function).
lanczos-sum-scaled (function).
lbeta (function).
lgam1p (function).
log-gamma (function).
log-ndtr (function).
log1p (function).
log1pmx (function).
nbdtr (function).
nbdtrc (function).
nbdtri (function).
ndtr (function).
ndtri (function).
owens-t (function).
pdtr (function).
pdtrc (function).
pdtri (function).
poch (function).
psi (function).
rgamma (function).
shichi (function).
sici (function).
sindg (function).
sinpi (function).
spence (function).
stdtr (function).
stdtri (function).
tandg (function).
y0 (function).
y1 (function).
yn (function).
yv (function).
zeta (function).
zetac (function).
cephes-airy (function).
cephes-ellpj (function).
cephes-fresnl (function).
cephes-shichi (function).
cephes-sici (function).
evlrat (function).
sign-gamma (function).
Definitions are sorted by export status, category, package, and then by lexicographic order.
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)
Returns the sum of the terms 0 through k of the Binomial probability density
Returns the sum of the terms k+1 through n of the Binomial probability density
Finds the event probability p such that the sum of the terms 0 through k of the Binomial probability density is equal to the given cumulative probability y.
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).
Returns the cube root of the argument, which may be negative.
Returns the area under the left hand tail (from 0 to x) of the Chi square probability density function with DF degrees of freedom.
Returns the area under the right hand tail (from x to infinity) of the Chi square probability density function with DF degrees of freedom
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
Range reduction is into intervals of 45 degrees.
Returns the circular cotangent of the argument x in degrees
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.
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.
Returns 10 raised to the x power.
Returns 2 raised to the x power.
Evaluates the exponential integral
Returns the area from zero to x under the F density function
Returns the area from x to infinity under the F density function
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
Returns Gamma function of the argument. The result is correctly signed.
Returns the integral from zero to x of the Gamma probability density function
Returns the integral from x to infinity of the Gamma probability density function
Computes the confluent hypergeometric function
Returns modified Bessel function of order zero of the argument
Returns exponentially scaled modified Bessel function of order zero of the argument
Returns modified Bessel function of order one of the argument
Returns exponentially scaled modified Bessel function of order one of the argument
Returns the x such that: igamc(a, x) = p
The input argument a must be positive and p must be between 0 and 1.
Returns incomplete beta integral of the arguments, evaluated from zero to x.
Given y, the function finds x such that incbet( a, b, x ) = y
Returns modified Bessel function of order v of the argument. If x is negative, v must be integer valued.
Returns Bessel function of order zero of the argument
Returns Bessel function of order one of the argument.
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)
Returns Bessel function of order v of the argument, where v is real. Negative x is allowed if v is an integer.
Returns modified Bessel function of the third kind of order zero of the argument.
Returns exponentially scaled modified Bessel function of the third kind of order zero of the argument.
Computes the modified Bessel function of the third kind of order one of the argument.
Returns exponentially scaled modified Bessel function of the third kind of order one of the argument
Returns modified Bessel function of the third kind of order n of the argument
Returns the base e logarithm of the absolute value of the Gamma function of the argument.
Returns the sum of the terms 0 through k of the negative binomial distribution
Returns the sum of the terms k+1 to infinity of the negative binomial distribution
Returns the sum of the terms k+1 to infinity of the negative binomial distribution
Returns the area under the Gaussian probability density function, integrated from minus infinity to x
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).
Returns the sum of the first k terms of the Poisson distribution
Returns the sum of the terms k+1 to infinity of the Poisson distribution
Finds the Poisson variable x such that the integral from 0 to x of the Poisson density is equal to the given probability y
Returns the logarithmic derivative of the gamma function
Returns one divided by the Gamma function of the argument
Returns VALUES (si ci)
Returns VALUES (si ci)
Range reduction is into intervals of 45 degrees.
Computes the integral from minus infinity to t of the Student t distribution with integer k > 0 degrees of freedom
Given probability p, finds the argument t such that stdtr(k,t) is equal to p
Returns the circular tangent of the argument x in degrees
Bessel function of the second kind, order zero
Returns Bessel function of the second kind of order one of the argument.
Returns Bessel function of order n, where n is a (possibly negative) integer
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).
Evaluates S and C fresnel integrals and returns VALUES (S C)
Evaluate a rational function
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