Initially Known Mathematical Functions - Maple Help

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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

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Two-argument arctan:  arctany,x=argumentx+Iy  in  π,π

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For more complete information regarding any of the functions <f> shown here, see ?<f> (for example, ?abs ).

abs

- absolute value of real or complex number

AiryAi,

- Airy wave functions and their negative real zeros

AiryAiZeros,

 

AiryBi,

 

AiryBiZeros

 

AngerJ

- Anger J function

argument

- argument of a complex number

BellB

- Bell polynomials

bernoulli

- Bernoulli numbers and polynomials

BesselI

- modified Bessel function of the first kind

BesselJ

- Bessel function of the first kind

BesselJZeros

- non-negative real zeros of Bessel J

BesselK

- modified Bessel function of the second kind

BesselY

- Bessel function of the second 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 first kind

ChebyshevU

- Chebyshev function of the second kind

Chi

- hyperbolic cosine integral

Ci

- cosine integral

CompleteBellB

- complete Bell polynomials

conjugate

- conjugate of a complex number or expression

CoulombF

- regular Coulomb wave function

CylinderD

- Whittaker's parabolic function

CylinderU,

- Parabolic cylinder functions

CylinderV

 

csgn

- complex "half-plane" signum function

dilog

- dilogarithm function

Dirac

- Dirac delta function

doublefactorial

- double factorial function

Ei

- exponential integrals

EllipticCE

- complementary complete elliptic integral of the second kind

EllipticCK

- complementary complete elliptic integral of the first kind

EllipticCPi

- complementary complete elliptic integral of the third kind

EllipticE

- incomplete or complete elliptic integral of the second kind

EllipticF

- incomplete elliptic integral of the first kind

EllipticK

- complete elliptic integral of the first kind

EllipticModulus

- Modulus elliptic function

EllipticNome

- Nome elliptic function

EllipticPi

- incomplete or complete elliptic integral of the third 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,

- Hankel functions (Bessel functions of the third kind)

HankelH2

 

harmonic

- partial sum of the harmonic series

Heaviside

- Heaviside step function

HermiteH

- Hermite function

HeunB,

- Heun functions

HeunC,

 

HeunD,

 

HeunG,

 

HeunT

 

HeunBPrime,

- derivatives of Heun functions

HeunCPrime,

 

HeunDPrime,

 

HeunGPrime,

 

HeunTPrime

 

hypergeom

- generalized hypergeometric function

ilog2,

- integer logarithms

ilog10,

 

ilog

 

Im

- imaginary part of a complex number

IncompleteBellB

- incomplete Bell polynomials

InverseJacobiAM

- inverse Jacobi amplitude function

InverseJacobiCD,

- inverse Jacobi elliptic functions

InverseJacobiCN,

 

InverseJacobiCS,

 

InverseJacobiDC,

 

InverseJacobiDN,

 

InverseJacobiDS,

 

InverseJacobiNC,

 

InverseJacobiND,

 

InverseJacobiNS,

 

InverseJacobiSC,

 

InverseJacobiSD,

 

InverseJacobiSN

 

JacobiP

- Jacobi function

JacobiAM

- Jacobi amplitude function

JacobiCD,

- Jacobi elliptic functions

JacobiCN,

 

JacobiCS,

 

JacobiDC,

 

JacobiDN,

 

JacobiDS,

 

JacobiNC,

 

JacobiND,

 

JacobiNS,

 

JacobiSC,

 

JacobiSD,

 

JacobiSN

 

JacobiTheta1,

- Jacobi theta functions

JacobiTheta2,

 

JacobiTheta3,

 

JacobiTheta4

 

JacobiZeta

- Jacobi Zeta function

KelvinBei,

- Kelvin functions

KelvinBer,

 

KelvinHei,

 

KelvinHer,

 

KelvinKei,

 

KelvinKer

 

KummerM,

- Kummer functions

KummerU

 

LaguerreL

- Laguerre function

LambertW

- Lambert W function

LegendreP

- associated Legendre function of the first kind

LegendreQ

- associated Legendre function of the second kind

LerchPhi

- Lerch's Phi function

Li

- logarithmic integral

ln

- natural logarithm (logarithm with base &ExponentialE; = 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

- first derivative of MathieuC

MathieuCE

- even 2π-periodic Mathieu function

MathieuCEPrime

- first derivative of MathieuCE

MathieuExponent

- Mathieu characteristic exponent

MathieuFloquet

- Floquet solution of Mathieu's equation

MathieuFloquetPrime

- first derivative of MathieuFloquet

MathieuS

- odd general Mathieu function

MathieuSPrime

- first derivative of MathieuS

MathieuSE

- odd 2π-periodic Mathieu function

MathieuSEPrime

- first derivative of MathieuSE

MeijerG

- MeijerG function

max

- maximum of a sequence of real values

min

- minimum of a sequence of real values

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

SphericalY

- spherical harmonic function

sqrt

- square root

Ssi

- shifted sine integral

Stirling1

- Stirling number of the first kind

Stirling2

- Stirling number of the second kind

StruveH

- Struve function

StruveL

- modified Struve function

surd

- non-principal root function

trunc

- nearest integer to a number in the direction of 0

unwindK

- unwinding number

WeberE

- Weber E function

WeierstrassP

- Weierstrass P-function

WeierstrassPPrime

- Derivative of Weierstrass P-function

WeierstrassSigma

- Weierstrass sigma-function

WeierstrassZeta

- Weierstrass zeta-function

WhittakerM,

- Whittaker functions

WhittakerW

 

Wrightomega

- Wright omega function

Zeta

- Riemann and Hurwitz zeta functions

• 

Additional mathematical 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

diff, evalc, evalf, expand, float, FunctionAdvisor, index[package], Initially Known Constants and Environment Variables, MathematicalFunctions, series, simplify, ?<fcn> where <fcn> is any of the functions listed above


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