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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