C....... ELEMENTARY AND SPECIAL FUNCTIONS (search also class L5)
C1..... Integer-valued functions (e.g., floor, ceiling, factorial, binomial coefficient)
BINOM Evaluate the binomial coefficient.
FAC Evaluate the factorial of the argument.
C2..... Powers, roots, reciprocals
CCBRT Evaluate the complex cube root.
INITS Initialize the orthogonal series so the function value is the number of terms needed to insure the error is no larger than the requested accuracy.
CSEVL Evaluate the N-term Chebyshev series.
C4..... Elementary transcendental functions
C4a Trigonometric, inverse trigonometric
CACOS Evaluate the complex arc cosine.
CARG Evaluate the argument of a complex number.
CASIN Evaluate the complex arc sine.
CATAN Evaluate the complex arc tangent.
CATAN2 Evaluate the complex arc tangent of a ratio.
CCOT Evaluate the complex cotangent.
COSDG Evaluate the cosine for the argument in degrees.
SINDG Evaluate the sine for the argument in degrees.
C4b.... Exponential, logarithmic
ALNREL Evaluate the natural logarithm of one plus the argument.
CEXPRL Evaluate the complex exponential function factored from first order.
CLNREL Evaluate the principal value of the complex natural logarithm of one plus the argument.
CLOG10 Evaluate the principal value of the complex common logarithm.
EXPRL Evaluate the exponential function factored from first order, (EXP(X) - 1.0)/X.
C4c.... Hyperbolic, inverse hyperbolic
ACOSH Evaluate the arc hyperbolic cosine.
ASINH Evaluate the arc hyperbolic sine.
ATANH Evaluate the arc hyperbolic tangent.
CACOSH Evaluate the complex arc hyperbolic cosine.
CASINH Evaluate the complex arc hyperbolic sine.
CATANH Evaluate the complex arc hyperbolic tangent.
CCOSH Evaluate the complex hyperbolic cosine.
CSINH Evaluate the complex hyperbolic sine.
CTAN Evaluate the complex tangent.
CTANH Evaluate the complex hyperbolic tangent.
C5..... Exponential and logarithmic integrals
ALI Evaluate the logarithmic integral.
CHI Evaluate the hyperbolic cosine integral.
CI Evaluate the cosine integral.
CIN Evaluate a function closely related to the cosine integral.
CINH Evaluate a function closely related to the hyperbolic cosine integral.
E1 Evaluate the exponential integral for arguments greater than zero and the Cauchy principal value of the integral for arguments less than zero.
EI Evaluate the exponential integral for arguments greater than zero and the Cauchy principal value for arguments less than zero.
ENE Evaluate the exponential integral of integer order for arguments greater than zero scaled by EXP(X).
SHI Evaluate the hyperbolic sine integral.
SI Evaluate the sine integral.
C7a.... Gamma, log gamma, reciprocal gamma
ALGAMS Return the logarithm of the absolute value of the gamma function and the sign of gamma.
ALNGAM Evaluate the logarithm of the absolute value of the gamma function.
CGAMMA Evaluate the complex gamma function.
CGAMR Evaluate the reciprocal complex gamma function.
CLNGAM Evaluate the complex natural logarithm of the gamma function.
GAMMA Evaluate the complete gamma function.
GAMR Evaluate the reciprocal gamma function.
POCH Evaluate a generalization of Pochhammer's symbol.
POCH1 Evaluate a generalization of Pochhammer's symbol starting from the first order.
ALBETA Evaluate the natural logarithm of the complete beta function for positive arguments.
BETA Evaluate the complete beta function.
CBETA Evaluate the complex complete beta function.
CLBETA Evaluate the complex logarithm of the complete beta function.
CPSI Evaluate the logarithmic derivative of the gamma function for a complex argument.
PSI Evaluate the logarithmic derivative of the gamma function.
CHIDF Evaluate the chi-squared distribution function.
CHIIN Evaluate the inverse of the chi-squared distribution function.
GAMDF Evaluate the gamma distribution function.
GAMI Evaluate the incomplete gamma function.
GAMIC Evaluate the complementary incomplete gamma function.
GAMIT Evaluate the Tricomi form of the incomplete gamma function.
BETAI Evaluate the incomplete beta function ratio.
BETDF Evaluate the beta probability distribution function.
BETIN Evaluate the inverse of the beta distribution function.
C8a.... Error functions, their inverses, integrals, including the normal distribution function
ANORDF Evaluate the standard normal (Gaussian) distribution function.
ANORIN Evaluate the inverse of the standard normal (Gaussian) distribution function.
CERFE Evaluate the complex scaled complemented error function.
ERF Evaluate the error function.
ERFC Evaluate the complementary error function.
ERFCE Evaluate the exponentially scaled complementary error function.
ERFCI Evaluate the inverse complementary error function.
ERFI Evaluate the inverse error function.
FRESC Evaluate the cosine Fresnel integral.
FRESS Evaluate the sine Fresnel integral.
DAWS Evaluate Dawson function.
C10a1 Real argument, integer order
BSJ0 Evaluate the Bessel function of the first kind of order zero.
BSJ1 Evaluate the Bessel function of the first kind of order one.
BSJNS Evaluate a sequence of Bessel functions of the first kind with integer order and real arguments.
BSY0 Evaluate the Bessel function of the second kind of order zero.
BSY1 Evaluate the Bessel function of the second kind of order one.
C10a2 Complex argument, integer order.
CBJNS Evaluate a sequence of Bessel functions of the first kind with integer order and complex arguments.
C10a3 Real argument, real order
BSJS Evaluate a sequence of Bessel functions of the first kind with real order and real positive arguments.
BSYS Evaluate a sequence of Bessel functions of the second kind with real nonnegative order and real positive arguments.
C10a4 Complex argument, real order
CBJS Evaluate a sequence of Bessel functions of the first kind with real order and complex arguments.
CBYS Evaluate a sequence of Bessel functions of the second kind with real order and complex arguments.
C10b1 Real argument, integer order
BSI0 Evaluate the modified Bessel function of the first kind of order zero.
BSI0E Evaluate the exponentially scaled modified Bessel function of the first kind of order zero.
BSI1 Evaluate the modified Bessel function of the first kind of order one.
BSI1E Evaluate the exponentially scaled modified Bessel function of the first kind of order one.
BSINS Evaluate a sequence of Modified Bessel functions of the first kind with integer order and real arguments.
BSK0 Evaluate the modified Bessel function of the third kind of order zero.
BSK0E Evaluate the exponentially scaled modified Bessel function of the third kind of order zero.
BSK1 Evaluate the modified Bessel function of the third kind of order one.
BSK1E Evaluate the exponentially scaled modified Bessel function of the third kind of order one.
C10b2 Complex argument, integer order
CBINS Evaluate a sequence of Modified Bessel functions of the first kind with integer order and complex arguments.
C10b3 Real argument, real order
BSIES Evaluate a sequence of exponentially scaled Modified Bessel functions of the first kind with nonnegative real order and real positive arguments.
BSIS Evaluate a sequence of Modified Bessel functions of the first kind with real order and real positive arguments.
BSKES Evaluate a sequence of exponentially scaled modified Bessel functions of the third kind of fractional order.
BSKS Evaluate a sequence of modified Bessel functions of the third kind of fractional order.
C10b4 Complex argument, real order
CBIS Evaluate a sequence of Modified Bessel functions of the first kind with real order and complex arguments.
CBKS Evaluate a sequence of Modified Bessel functions of the second kind with real order and complex arguments.
AKEI0 Evaluate the Kelvin function of the second kind, kei, of order zero.
AKEI1 Evaluate 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 Evaluate the Kelvin function of the second kind, ker, of order zero.
AKER1 Evaluate the Kelvin function of the second kind, ker, of order one.
AKERP0 Evaluate the derivative of the Kelvin function of the second kind, ker, of order zero.
BEI0 Evaluate the Kelvin function of the first kind, bei, of order zero.
BEI1 Evaluate the Kelvin function of the first kind, bei, of order one.
BEIP0 Evaluate the derivative of the Kelvin function of the first kind, bei, of order zero.
BER0 Evaluate the Kelvin function of the first kind, ber, of order zero.
BER1 Evaluate the Kelvin function of the first kind, ber, of order one.
BERP0 Evaluate the derivative of the Kelvin function of the first kind, ber, of order zero.
C10d.. Airy and Scorer functions
AI Evaluate the Airy function.
AID Evaluate the derivative of the Airy function.
AIDE Evaluate the exponentially scaled derivative of the Airy
AIE Evaluate the exponentially scaled Airy function.
BI Evaluate the Airy function of the second kind.
BID Evaluate the derivative of the Airy function of the second kind.
BIDE Evaluate the exponentially scaled derivative of the Airy function of the second kind.
BIE Evaluate the exponentially scaled Airy function of the second kind.
CEJCN Evaluate the complex Jacobi elliptic integral cn(z, m).
CEJDN Evaluate the complex Jacobi elliptic integral dn(z, m).
CEJSN Evaluate the complex Jacobi elliptic function sn(z, m).
EJCN Evaluate the Jacobi elliptic function cn(x, m).
EJDN Evaluate the Jacobi elliptic function dn(x, m).
EJSN Evaluate the Jacobi elliptic function sn(x, m).
ELE Evaluate the complete elliptic integral of the second kind E(x).
ELK Evaluate the complete elliptic integral of the kind K(x).
ELRC Evaluate an elementary integral from which inverse circular functions, logarithms and inverse hyperbolic functions can be computed.
ELRD Evaluate Carlson's incomplete elliptic integral of the second kind RD(X, Y, Z).
ELRF Evaluate Carlson's incomplete elliptic integral of the first kind RF(X, Y, Z).
ELRJ Evaluate Carlson's incomplete elliptic integral of the third kind RJ(X, Y, Z, RHO).
C15.... Weierstrass elliptic functions
CWPL Evaluate 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 Evaluate the Weierstrass P-function in the equianharmonic case for complex argument with unit period parallelogram.
CWPQD Evaluate the first derivative of the Weierstrass P-function in the equianharmonic case for complex argument with unit period parallelogram.
MATCE Evaluate a sequence of even, periodic, integer order, real Mathieu functions.
MATEE Evaluate the eigenvalues for the periodic Mathieu functions.
MATSE Evaluate a sequence of odd, periodic, integer order, real Mathieu functions.
C19.... Other special functions
SPENC Evaluate a form of Spence's integral.
L....... STATISTICS, PROBABILITY
L5...... Function evaluation (search also class C)
L5a1.. Cumulative distribution functions, probability density functions
GCDF Evaluate a general continuous cumulative distribution function given ordinates of the density.
BETDF Evaluate the beta probability distribution function.
BINDF Evaluate the binomial distribution function.
BINPR Evaluate the binomial probability function.
CHIDF Evaluate the chi-squared distribution function.
CSNDF Evaluate the noncentral chi-squared distribution function.
FDF Evaluate the F distribution function.
L5a1g. Gamma, general, geometric
GAMDF Evaluate the gamma distribution function.
L5a1h. Halfnormal, hypergeometric
HYPDF Evaluate the hypergeometric distribution function.
HYPPR Evaluate the hypergeometric probability function.
L5a1k. Kendall F statistic, Kolmogorov-Smirnov
AKS1DF Evaluate the distribution function of the one-sided Kolmogorov-Smirnov goodness of fit D+ or D− test statistic based on continuous data for one sample.
AKS2DF Evaluate the distribution function of the Kolmogorov-Smirnov goodness of fit D test statistic based on continuous data for two samples.
L5a1n. Negative binomial, normal
ANORDF Evaluate the standard normal (Gaussian) distribution function.
POIDF Evaluate the Poisson distribution function.
POIPR Evaluate the Poisson probability function.
TDF Evaluate the Student's t distribution function.
TNDF Evaluate the noncentral Student's t distribution function.
L5a2.. Inverse cumulative distribution functions, sparsity functions
GCIN Evaluate the inverse of a general continuous cumulative distribution function given ordinates of the density.
BETIN Evaluate the inverse of the beta distribution function.
CHIIN Evaluate the inverse of the chi-squared distribution function.
FIN Evaluate the inverse of the F distribution function.
L5a2n. Negative binomial, normal, normal scores
ANORIN Evaluate the inverse of the standard normal (Gaussian) distribution function.
TIN Evaluate the inverse of the Student's t distribution function.
L5b1.. Cumulative distribution functions, probability density functions
BNRDF Evaluate the bivariate normal distribution function.
IFNAN Check if a value is NaN (not a number).
N4..... Storage management (e.g., stacks, heaps, trees)
IWKCIN Initialize bookkeeping locations describing the character workspace stack.
IWKIN Initialize bookkeeping locations describing the workspace stack.
R1..... Machine-dependent constants
AMACH Retrieve single-precision machine constants.
DMACH Retrieve double precision machine constants.
IFNAN Check if a value is NaN (not a number).
IMACH Retrieve integer machine constants.
UMACH Set or retrieve input or output device unit numbers.
ERSET Set error handler default print and stop actions.
IERCD Retrieve the code for an informational error.
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