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CEPHES Package

Functions listed in the following table are straight forward wrapping of CEPHES library functions. These functions are called as .cephes("func", a, b, c,...) Please refer to http://www.moshier.net or this link for details.

Function Remark
bdtr(k, n, p) Returns Returns the sum of the terms 0 through k of the Binomial probability density.
bdtrc(k, n, p) Returns the sum of the terms k+1 through n of the Binomial probability density.
bdtri(k, n, p) 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.
beta(a, b) Beta function.
btdtr(a, b, x) Returns the area from zero to x under the beta density function.
cbrt(x) Returns the cube root of the argument, which may be negative.
chbevl(x, coef) Evaluates the series of Chebyshev polynomials. The argument coef is the a 1D-zeArray of double type.
chdtr(df, x) Returns the area under the left hand tail (from 0 to x) of the Chi square probability density function.
chdtrc(v, x) Returns the area under the right hand tail (from x to infinity) of the Chi square probability density 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.
dawsn(x) Dawson's integral.
drand(d) Returns a random number 1.0 <= d < 2.0
ei(x) Exponential integral.
ellie(phi, m) Incomplete elliptic integral of the second kind.
ellik(phi, m) Incomplete elliptic integral of the first kind.
ellpe(m1) Complete elliptic integral of the second kind.
ellpj(u, m, sn, cn, dn, phi) 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.
ellpk(m1) Complete elliptic integral of the first kind.
expn(n, x) Exponential integral.
fac(i) Factorial function.
fdtr(df1, df2, x) F distribution.
fdtrc(df1, df2, x) Complemented F distribution.
fdtri(df1, df2, p) Inverse of complemented F distribution.
fresnl(x) Returns the Fresnel integrals.
gamma(x) Returns gamma function of the argument.
lgam(x) Natural logarithm of gamma function.
gdtr(a, b, x) Returns the integral from zero to x of the gamma probability density function.
gdtrc(a, b, x) Returns the integral from x to infinity of the gamma probability density function.
hyp2f1( a, b, c, x) Gauss hypergeometric function.
hyperg(a, b, x) Confluent hypergeometric function.
i0(x) Returns modified Bessel function of order zero of the argument.
i0e(x) Returns exponentially scaled modified Bessel function of order zero of the argument.
i1(x) Returns modified Bessel function of order one of the argument.
i1e(x) Returns exponentially scaled modified Bessel function of order one of the argument.
igam(a, x) Incomplete gamma integral.
igamc(a, x) Complemented incomplete gamma integral.
igami(a, p) Inverse of complemented imcomplete gamma integral.
incbet(a, b, x) Incomplete beta integral.
incbi(a, b, y) Inverse of imcomplete beta integral.
iv(v, x) Returns modified Bessel function of order v of the argument.
j0(x) Returns Bessel function of order zero of the argument.
y0(x) Returns Bessel function of the second kind, of order zero, of the argument.
j1(x) Returns Bessel function of order one of the argument.
y1(x) Returns Bessel function of the second kind of order one of the argument.
jn(n, x) Returns Bessel function of order n.
jv(v, x) Returns Bessel function of order v of the argument.
k0(x) Returns modified Bessel function of the third kind of order zero of the argument.
k0e(x) Returns exponentially scaled modified Bessel function of the third kind of order zero of the argument.
k1(x) Returns the modified Bessel function of the third kind of order one of the argument.
k1e(x) Returns exponentially scaled modified Bessel function of the third kind of order one of the argument.
kn(n, x) Returns modified Bessel function of the third kind of order n of the argument.
lrand(l) Returns a long integer random number.
nbdtr(k, n, p) Returns the sum of the terms 0 through k of the negative binomial distribution.
nbdtrc(k, n, p) Returns the sum of the terms k+1 to infinity of the negative binomial distribution.
nbdtri(k, n, y) Finds the argument p such that nbdtr(k,n,p) is equal to y.
ndtr(x) Returns the area under the Gaussian probability density function, integrated from minus infinity to x.
erf(x) Error function.
erfc(x) Complementary error function.
ndtri(y) Returns the argument, x, for which the area under the Gaussian probability density function (integrated from minus infinity to x) is equal to y.
pdtr(k, m) Returns the sum of the first k terms of the Poisson distribution.
pdtrc(k, m) Returns the sum of the terms k+1 to infinity of the Poisson distribution.
pdtri(k, m) Finds the Poisson variable x such that the integral from 0 to x of the Poisson density is equal to the given probability y.
plancki(lambda, T) Evaluates the definite integral, from wavelength 0 to lambda, of Planck's radiation formula
psi(x) Psi (digamma) function.
polylog(n, x) Polylogarithm.
rgamma(x) Returns one divided by the gamma function of the argument.
shichi(x) Returns hyperbolic sine and cosine integrals.
sici(x) Return sine and cosine integrals.
spence(x) Dilogarithm.
stdtr(k, t) Computes the integral from minus infinity to t of the Student t distribution with integer k > 0 degrees of freedom.
stdtri(k, t) Given probability p, finds the argument t such that stdtr(k,t) is equal to p.
struve(v, x) Computes the Struve function Hv(x) of order v, argument x.
yn(n, x) Returns Bessel function of order n, where n is a (possibly negative) integer.
zeta(x, q) Riemann zeta function of two arguments.
zetac(x, q) Riemann zeta function.