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. |