# Initially-known mathematical functions in Maple  (copied from the Maple help file)

These mathematical functions are known to Maple, in that they have simplification procedures defined and/or are known to one or more of: diff, evalc, evalf, expand, series, simplify

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 abs - absolute value of real or complex number AiryAi AiryAiZeros AiryBi AiryBiZeros - Airywave functions and their negative real zeros AngerJ - Anger J function argument -argument of a complex number bernoulli -Bernoulli numbers and polynomials BesselI BesselJ - modified Bessel functions and Bessel functions of the 1st kind BesselJZeros - non negative realzeros of Bessel J BesselK BesselY - modified Bessel functions and Bessel functions of the 2nd kind BesselYZeros - positive realzeros of Bessel Y Beta - Beta function binomial - binomial coefficients ceil - smallest integer greater than or equal to a number Chi - hyperbolic cosine integral Ci - cosine integral conjugate -conjugate of a complex number or expression csgn - complex ``half-plane'' signum function dilog - dilogarithm function Dirac - Dirac delta function Ei - exponential integrals EllipticCE EllipticCK EllipticCPi EllipticE EllipticF EllipticK EllipticModulus EllipticNome EllipticPi - Complete incomplete and complementary elliptic integrals and related functions erf - error function erfc - complementary error function and its iterated integrals erfi - imaginary error function euler - Euler numbers and polynomials exp - exponential function factorial -factorial function floor - greatest integer less than or equal to a number frac - fractional part of a number FresnelC Fresnelf Fresnelg FresnelS - Fresnel integrals and auxiliary functions GAMMA - Gamma and incomplete Gamma functions GaussAGM - Gauss arithmetic geometric mean HankelH1 HankelH2 - Hankel functions (Bessel functions of the 3rd kind) harmonic - partial sum of the harmonic series Heaviside - Heaviside step function hypergeom - generalized hypergeometric function ilog10 ilog - integer logarithms Im - imaginary part of a complex number JacobiAM JacobiCN JacobiCD JacobiCS JacobiDN JacobiDC JacobiDS JacobiNC JacobiND JacobiNS JacobiSC JacobiSD JacobiSN - Jacobi elliptic functions JacobiTheta1 JacobiTheta2 JacobiTheta3 JacobiTheta4 - Jacobi theta functions JacobiZeta -Jacobi Zeta function KelvinBer KelvinBei KelvinHer KelvinHei KelvinKer KelvinKei -Kelvin functions KummerM KummerU - Kummer functions LegendreP LegendreQ -Legendre functions LerchPhi - Lerch's Phi function Li - logarithmic integral ln - natural logarithm (logarithm with base  exp(1) = 2.71...) lnGAMMA - log-Gamma function log - logarithm to arbitrary base log10 - log to the base 10 LommelS1 LommelS2 - Lommel functions MeijerG - a modified MeijerG function max min - maximum/minimum of a sequence of real values pochhammer - pochhammersymbol polar - polar representation of complex numbers polylog - polylogarithm function Psi - polygamma function Re - real part of a complex number round - nearest integer to a number signum - sign of a real or complex number Shi - hyperbolic sine integral Si - sine integral sqrt - square root Ssi - shifted sine integral StruveH StruveL - Struve functions surd - non-principal root function trunc - nearest integer to a number in the direction of 0 LambertW - Lambert W function WeberE - Weber E function WeierstrassP - WeierstrassP-function WeierstrassPPrime - Derivative of Weierstrass P-function WeierstrassZeta - Weierstrass zeta-function WeierstrassSigma - Weierstrass sigma-function WhittakerM WhittakerW -Whittaker functions Zeta - Riemann and Hurwitz zeta functions

The trigonometric and hyperbolic functions:
sin,  cos,  tan,  sec,
csc,  cot,  sinh, cosh,
tanh, sech, csch, coth

The inverse trigonometric and inverse hyperbolic functions:
arcsin,  arccos,  arctan,  arcsec,  arccsc,  arccot,
arcsinh, arccosh, arctanh, arcsech, arccsch, arccoth

two-argument arctan: arctan(y,x) = argument(x+I*y) in (-Pi,Pi]

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Agnes Szanto