ACOS

Evaluates the complex arc cosine.

ACOSH

Evaluates the real or complex arc hyperbolic cosine.

AI

Evaluates the Airy function.

AID

Evaluates the derivative of the Airy function.

AIDE

Evaluates the Airy function of the second kind.

AIE

Evaluates the exponentially scaled derivative of the Airy function.

AKEI0

Evaluates the Kelvin function of the second kind, kei, of order zero.

AKEI1

Evaluates the Kelvin function of the second kind, kei, of order one.

AKEIP0

Evaluates the derivative of the Kelvin function of the second kind, kei, of order zero.

AKER0

Evaluates the Kelvin function of the second kind, ker, of order zero.

AKER1

Evaluates the Kelvin function of the second kind, ker, of order one.

AKERP0

Evaluates the derivative of the Kelvin function of the second kind, ker, of order zero.

AKS1DF

Evaluates the cumulative distribution function of the one-sided Kolmogorov-Smirnov goodness of fit D+ or D− test statistic based on continuous data for one sample.

AKS2DF

Evaluates the cumulative distribution function of the Kolmogorov-Smirnov goodness of fit D test statistic based on continuous data for two samples.

ALBETA

Evaluates the natural logarithm of the complete beta function for positive arguments.

ALGAMS

Returns the logarithm of the absolute value of the gamma function and the sign of gamma.

ALI

Evaluates the logarithmic integral.

ALNDF

Evaluates the lognormal cumulative probability distribution function

ALNGAM

Evaluates the real or complex function, ln |γ(x)|.

ALNIN

Evaluates the inverse of the lognormal cumulative probability distribution function.

ALNPR

Evaluates the lognormal probability density function.

ALNREL

Evaluates ln(x + 1) for real or complex x.

AMACH

Retrieves single-precision machine constants.

ANORDF

Evaluates the standard normal (Gaussian) cumulative distribution function.

ANORPR

Evaluates the normal probability density function.

ANORIN

Evaluates the inverse of the standard normal (Gaussian) cumulative distribution function.

ASIN

Evaluates the complex arc sine.

ASINH

Evaluates the sinh−1 arc sine x for real or complex x.

ATAN

Evaluates the complex arc tangent.

ATAN2

Evaluates the complex arc tangent of a ratio.

ATANH

Evaluates tanh−1 x for real or complex x.

BEI0

Evaluates the Kelvin function of the first kind, bei, of order zero.

BEI1

Evaluates the Kelvin function of the first kind, bei, of order one.

BEIP0

Evaluates the derivative of the Kelvin function of the first kind, bei, of order zero.

BER0

Evaluates the Kelvin function of the first kind, ber, of order zero.

BER1

Evaluates the Kelvin function of the first kind, ber, of order one.

BERP0

Evaluates the derivative of the Kelvin function of the first kind, ber, of order zero.

BETA

Evaluates the real or complex beta function, β(a,b).

BETAI

Evaluates the incomplete beta function ratio.

BETDF

Evaluates the the beta cumulative distribution function.

BETIN

Evaluates the inverse of the beta cumulative distribution function.

BETNDF

Evaluates the beta cumulative distribution function.

BETNIN

Evaluates the inverse of the beta cumulative distribution function.

BETNPR

This function evaluates the noncentral beta probability density function.

BETPR

Evaluates the beta probability density function.

BI

Evaluates the Airy function of the second kind.

BID

Evaluates the derivative of the Airy function of the second kind.

BIDE

Evaluates the exponentially scaled derivative of the Airy function of the second kind.

BIE

Evaluates the exponentially scaled Airy function of the second kind.

BINDF

Evaluates the binomial cumulative distribution function.

BINOM

Evaluates the binomial coefficient.

BINPR

Evaluates the binomial probability density function.

BNRDF

Evaluates the bivariate normal cumulative distribution function.

BSI0

Evaluates the modified Bessel function of the first kind of order zero.

BSI0E

Evaluates the exponentially scaled modified Bessel function of the first kind of order zero.

BSI1

Evaluates the modified Bessel function of the first kind of order one.

BSI1E

Evaluates the exponentially scaled modified Bessel function of the first kind of order one.

BSIES

Evaluates a sequence of exponentially scaled modified Bessel functions of the first kind with nonnegative real order and real positive arguments.

BSINS

Evaluates a sequence of modified Bessel functions of the first kind with integer order and real or complex arguments.

BSIS

Evaluates a sequence of modified Bessel functions of the first kind with real order and real positive arguments.

BSJ0

Evaluates the Bessel function of the first kind of order zero.

BSJ1

Evaluates the Bessel function of the first kind of order one.

BSJNS

Evaluates a sequence of Bessel functions of the first kind with integer order and real arguments.

BSJS

Evaluates a sequence of Bessel functions of the first kind with real order and real positive arguments.

BSK0

Evaluates the modified Bessel function of the second kind of order zero.

BSK0E

Evaluates the exponentially scaled modified Bessel function of the second kind of order zero.

BSK1

Evaluates the modified Bessel function of the second kind of order one.

BSK1E

Evaluates the exponentially scaled modified Bessel function of the second kind of order one.

BSKES

Evaluates a sequence of exponentially scaled modified Bessel functions of the second kind of fractional order.

BSKS

Evaluates a sequence of modified Bessel functions of the second kind of fractional order.

BSY0

Evaluates the Bessel function of the second kind of order zero.

BSY1

Evaluates the Bessel function of the second kind of order one.

BSYS

Evaluates a sequence of Bessel functions of the second kind with real nonnegative order and real positive arguments.

CAI

Evaluates the Airy function of the first kind for complex arguments.

CAID

Evaluates the derivative of the Airy function of the first kind for complex arguments.

CARG

Evaluates the argument of a complex number.

CBI

Evaluates the Airy function of the second kind for complex arguments.

CBID

Evaluates the derivative of the Airy function of the second kind for complex arguments.

CBIS

Evaluates a sequence of modified Bessel functions of the first kind with real order and complex arguments.

CBJS

Evaluates a sequence of Bessel functions of the first kind with real order and complex arguments.

CBKS

Evaluates a sequence of Modified Bessel functions of the second kind with real order and complex arguments.

CBRT

Evaluates the cube root.

CBYS

Evaluates a sequence of Bessel functions of the second kind with real order and complex arguments.

CERFE

Evaluates the complex scaled complemented error function.

CHI

Evaluates the hyperbolic cosine integral.

CHIDF

Evaluates the chi-squared cumulative distribution function

CHIIN

Evaluates the inverse of the chi-squared cumulative distribution function.

CHIPR

Evaluates the chi-squared probability density function

CI

Evaluates the cosine integral.

CIN

Evaluates a function closely related to the cosine integral.

CINH

Evaluates a function closely related to the hyperbolic cosine integral.

COSDG

Evaluates the cosine for the argument in degrees.

COT

Evaluates the cotangent.

CSEVL

Evaluates the N-term Chebyshev series.

CSNDF

Evaluates the noncentral chi-squared cumulative distribution function.

CSNIN

Evaluates the inverse of the noncentral chi-squared cumulative function.

CSNPR

This function evaluates the noncentral chi-squared probability density function.

CWPL

Evaluates the Weierstrass P-function in the lemniscat case for complex argument with unit period parallelogram.

CWPLD

Evaluate the first derivative of the Weierstrass P-function in the lemniscatic case for complex argum with unit period parallelogram.

CWPQ

Evaluates the Weierstrass P-function in the equianharmonic case for complex argument with unit period parallelogram.

CWPQD

Evaluates the first derivative of the Weierstrass P-function in the equianharmonic case for complex argument with unit period parallelogram.

DAWS

Evaluates Dawson function.

DMACH

Retrieves double precision machine constants.

E1

Evaluates the exponential integral for arguments greater than zero and the Cauchy principal value of the integral for arguments less than zero.

EI

Evaluates the exponential integral for arguments greater than zero and the Cauchy principal value for arguments less than zero.

EJCN

Evaluates the Jacobi elliptic function cn(x, m).

EJDN

This function evaluates the Jacobi elliptic function dn(x, m).

EJSN

Evaluates the Jacobi elliptic function sn(x, m).

ELE

Evaluates the complete elliptic integral of the second kind E(x).

ELK

Evaluates the complete elliptic integral of the kind K(x).

ELRC

Evaluates an elementary integral from which inverse circular functions, logarithms and inverse hyperbolic functions can be computed.

ELRD

Evaluates Carlson's incomplete elliptic integral of the second kind RD(X, Y, Z).

ELRF

Evaluates Carlson's incomplete elliptic integral of the first kind RF(X, Y, Z).

ELRJ

Evaluates Carlson's incomplete elliptic integral of the third kind RJ(X, Y, Z, RHO).

ENE

Evaluates the exponential integral of integer order for arguments greater than zero scaled by EXP(X).

ERF

Evaluates the error function.

ERFC

Evaluates the complementary error function.

ERFCE

Evaluates the exponentially scaled complementary error function.

ERFCI

Evaluates the inverse complementary error function.

ERFI

Evaluates the inverse error function.

ERSET

Sets error handler default printer and stop actions.

EXPDF

Evaluates the exponential cumulative distribution function.

EXPIN

Evaluates the inverse of the exponential cumulative distribution function.

EXPPR

Evaluates the exponential probability density function.

EXPRL

Evaluates (ex – 1)/x for real or complex x.

EXVDF

Evaluates the extreme value cumulative distribution function.

EXVIN

Evaluates the inverse of the extreme value cumulative distribution function.

EXVPR

Evaluates the extreme value probability density function.

FAC

Evaluates the factorial of the argument.

FDF

Evaluates the F cumulative distribution function.

FIN

Evaluates the inverse of the F cumulative distribution function.

FNDF

Noncentral F cumulative distribution function.

FNIN

This function evaluates the inverse of the noncentral F cumulative distribution function (CDF).

FNPR

This function evaluates the noncentral F cumulative distribution function (CDF).

FPR

Evaluates the F probability density function.

FRESC

Evaluates the cosine Fresnel integral.

FRESS

Evaluates the sineFresnel integral.

GAMDF

Evaluates the gamma cumulative distribution function.

GAMI

Evaluates the incomplete gamma function.

GAMIC

Evaluates the complementary incomplete gamma function.

GAMIN

This function evaluates the inverse of the gamma cumulative distribution function.

GAMIT

Evaluates the Tricomi form of the incomplete gamma function.

GAMMA

Evaluates the real or complex gamma function, Γ(x).

GAMPR

This function evaluates the gamma probability density function.

GAMR

Evaluates the reciprocal of the real or complex gamma
function, 1/Γ(x).

GCDF

Evaluates a general continuous cumulative distribution function given ordinates of the density.

GCIN

Evaluates the inverse of a general continuous cumulative distribution function given ordinates of the density.

GEODF

Evaluates the discrete geometric cumulative probability distribution function.

GEOIN

Evaluates the inverse of the geometric cumulative probability distribution function.

GEOPR

Evaluates the discrete geometric probability density function.

GFNIN

Evaluates the inverse of a general continuous cumulative distribution function given in a subprogram.

HYPDF

Evaluates the hypergeometric cumulative distribution function.

HYPPR

Evaluates the hypergeometric probability density function.

IERCD and N1RTY

Retrieves the integer code for an informational error.

IFNAN(X)

Checks if a value is NaN (not a number).

IMACH

Retrieves integer machine constants.

INITS

Initializes the orthogonal series so the function value is the number of terms needed to insure the error is no larger than the requested accuracy.

LOG10

Evaluates the complex base 10 logarithm, log10 z.

MATCE

Evaluates a sequence of even, periodic, integer order, real Mathieu functions.

MATEE

Evaluates the eigenvalues for the periodic Mathieu functions.

MATSE

Evaluates a sequence of odd, periodic, integer order, real Mathieu functions.

IERCD and N1RTY

Retrieves the error type set by the most recently called IMSL routine.

POCH

Evaluates a generalization of Pochhammer's symbol.

POCH1

Evaluates a generalization of Pochhammer's symbol starting from the first order.

POIDF

Evaluates the Poisson cumulative distribution function.

POIPR

Evaluates the Poisson probability density function.

PSI

Evaluates the derivative of the log gamma function.

PSI1

Evaluates the second derivative of the log gamma function.

RALDF

Evaluates the Rayleigh cumulative distribution function.

RALIN

Evaluates the inverse of the Rayleigh cumulative distribution function.

RALPR

Evaluates the Rayleigh probability density function.

SHI

Evaluates the hyperbolic sine integral.

SI

Evaluates the sine integral.

SINDG

Evaluates the sine for the argument in degrees.

SPENC

Evaluates a form of Spence's integral.

TAN

Evaluates tan z for complex z.

TDF

Evaluates the Student's t cumulative distribution function.

TIN

Evaluates the inverse of the Student's t cumulative distribution function.

TNDF

Evaluates the noncentral Student's t cumulative distribution function.

TNIN

Evaluates the inverse of the noncentral Student's t cumulative distribution function.

TNPR

This function evaluates the noncentral Student's t probability density function.

TPR

Evaluates the Student's t probability density function.

UMACH

Sets or Retrieves input or output device unit numbers.

UNDF

Evaluates the uniform cumulative distribution function.

UNDDF

Evaluates the discrete uniform cumulative distribution function.

UNDIN

Evaluates the inverse of the discrete uniform cumulative distribution function.

UNDPR

Evaluates the discrete uniform probability density function.

UNIN

Evaluates the inverse of the uniform cumulative distribution function.

UNPR

Evaluates the uniform probability density function.

WBLDF

Evaluates the Weibull cumulative distribution function

WBLIN

Evaluates the inverse of the Weibull cumulative distribution function.

WBLPR

Evaluates the Weibull probability density function.