Initially Known Mathematical Functions Description 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. 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) For more complete information regarding any of the functionsshown here, see ? (for example, ?abs ). abs - absolute value of real or complex number AiryAi, AiryAiZeros, AiryBi, AiryBiZeros - Airy wave functions and their negative real zeros AngerJ - Anger J function argument - argument of a complex number bernoulli - Bernoulli numbers and polynomials BesselI - modified Bessel function of the 1st kind BesselJ - Bessel function of the 1st kind BesselJZeros - non negative real zeros of Bessel J BesselK - modified Bessel function of the 2nd kind BesselY - Bessel function of the 2nd kind BesselYZeros - positive real zeros of Bessel Y Beta - Beta function binomial - binomial coefficients ceil - smallest integer greater than or equal to a number ChebyshevT - Chebyshev function of the 1st kind ChebyshevU - Chebyshev function of the 2nd kind Chi - hyperbolic cosine integral Ci - cosine integral CylinderD - Whittaker's parabolic function CylinderU, CylinderV - Parabolic cylinder functions 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 - complementary complete elliptic integral of the 2nd kind EllipticCK - complementary complete elliptic integral of the 1st kind EllipticCPi - complementary complete elliptic integral of the 3rd kind EllipticE - incomplete or complete elliptic integral of the 2nd kind EllipticF - incomplete elliptic integral of the 1st kind EllipticK - complete elliptic integral of the 1st kind EllipticModulus - Modulus elliptic function EllipticNome - Nome elliptic function EllipticPi - incomplete or complete elliptic integral of the 3rd kind 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 - Fresnel cosine integral Fresnelf - Fresnel f auxiliary function Fresnelg - Fresnel g auxiliary function FresnelS - Fresnel sine integral GAMMA - Gamma and incomplete Gamma functions GaussAGM - Gauss arithmetic geometric mean GegenbauerC - Gegenbauer (ultraspherical) function HankelH1, HankelH2 - Hankel functions (Bessel functions of the 3rd kind) harmonic - partial sum of the harmonic series Heaviside - Heaviside step function HermiteH - Hermite function hypergeom - generalized hypergeometric function ilog2, ilog10, ilog - integer logarithms Im - imaginary part of a complex number InverseJacobiAM - inverse Jacobi amplitude function InverseJacobiCD, InverseJacobiCN, InverseJacobiCS, InverseJacobiDC, InverseJacobiDN, InverseJacobiDS, InverseJacobiNC, InverseJacobiND, InverseJacobiNS, InverseJacobiSC, InverseJacobiSD, InverseJacobiSN - inverse Jacobi elliptic functions JacobiP - Jacobi function JacobiAM - Jacobi amplitude function JacobiCD, JacobiCN, JacobiCS, JacobiDC, JacobiDN, JacobiDS, JacobiNC, JacobiND, JacobiNS, JacobiSC, JacobiSD, JacobiSN - Jacobi elliptic functions JacobiTheta1, JacobiTheta2, JacobiTheta3, JacobiTheta4 - Jacobi theta functions JacobiZeta - Jacobi Zeta function KelvinBei, KelvinBer, KelvinHei, KelvinHer, KelvinKei, KelvinKer - Kelvin functions KummerM, KummerU - Kummer functions LaguerreL - Laguerre function LambertW - Lambert W function LegendreP - associated Legendre function of the 1st kind LegendreQ - associated Legendre function of the 2nd kind 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 - Lommel function s LommelS2 - Lommel function S MathieuA - Mathieu characteristic function MathieuB - Mathieu characteristic function MathieuC - even general Mathieu function MathieuCPrime - 1st derivative of MathieuC MathieuCE - even 2*Pi-periodic Mathieu function MathieuCEPrime - 1st derivative of MathieuCE MathieuExponent - Mathieu characteristic exponent MathieuFloquet - Floquet solution of Mathieu's equation MathieuFloquetPrime - 1st derivative of MathieuFloquet MathieuS - odd general Mathieu function MathieuSPrime - 1st derivative of MathieuS MathieuSE - odd 2*Pi-periodic Mathieu function MathieuSEPrime - 1st derivative of MathieuSE MeijerG - MeijerG function max, min - maximum/minimum of a sequence of real values ModifiedMeijerG - a modified MeijerG function pochhammer - pochhammer symbol polar - polar representation of complex numbers polylog - polylogarithm function Psi - polygamma function Re - real part of a complex number RiemannTheta - Riemann theta function 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 - Struve function StruveL - modified Struve function surd - non-principal root function trunc - nearest integer to a number in the direction of 0 WeberE - Weber E function WeierstrassP - Weierstrass P-function WeierstrassPPrime - Derivative of Weierstrass P-function WeierstrassSigma - Weierstrass sigma-function WeierstrassZeta - Weierstrass zeta-function WhittakerM, WhittakerW - Whittaker functions Zeta - Riemann and Hurwitz zeta functions Additional math functions are defined in various packages, such as the combinatorial functions package combinat, the number theory package numtheory, and the orthogonal polynomial package orthopoly. For a complete list of packages, see index[package].
See Also: ininames, diff, evalc, evalf, expand, series, simplify, Float, index[package], ?<fcn> where <fcn> is any of the functions listed above
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