initially known functions - Maple Help

Home : Support : Online Help : Mathematics : General Information : initially known functions

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,

 • The inverse trigonometric and inverse hyperbolic functions:

 • Two-argument arctan:  $\mathrm{arctan}\left(y,x\right)=\mathrm{arg}\left(x+Iy\right)$  in  $\left(-\mathrm{\pi },\mathrm{\pi }\right)$
 • For more complete information regarding any of the functions shown here, see ? (for example, ?abs ).

 - absolute value of real or complex number - Airy wave functions and their negative real zeros - Anger J function Appell's doubly hypergeometric F functions - argument of a complex number - Bell polynomials - Bernoulli numbers and polynomials - modified Bessel function of the first kind - Bessel function of the first kind - non-negative real zeros of Bessel J - modified Bessel function of the second kind - Bessel function of the second kind - positive real zeros of Bessel Y - Beta function - binomial coefficients - smallest integer greater than or equal to a number - Chebyshev function of the first kind - Chebyshev function of the second kind - hyperbolic cosine integral - cosine integral - complete Bell polynomials - conjugate of a complex number or expression - regular Coulomb wave function - Whittaker's parabolic function - Parabolic cylinder functions - complex "half-plane" signum function - Dawson's integral - dilogarithm function - Dirac delta function - double factorial function - exponential integrals - complementary complete elliptic integral of the second kind - complementary complete elliptic integral of the first kind - complementary complete elliptic integral of the third kind - incomplete or complete elliptic integral of the second kind - incomplete elliptic integral of the first kind - complete elliptic integral of the first kind - Modulus elliptic function - Nome elliptic function - incomplete or complete elliptic integral of the third kind - error function - complementary error function and its iterated integrals - imaginary error function - Euler numbers and polynomials - exponential function - factorial function - greatest integer less than or equal to a number - fractional part of a number - Fresnel cosine integral - Fresnel f auxiliary function - Fresnel g auxiliary function - Fresnel sine integral - Gamma and incomplete Gamma functions - Gauss arithmetic geometric mean - Gegenbauer (ultraspherical) function - generalized polylogarithmic function - Hankel functions (Bessel functions of the third kind) - partial sum of the harmonic series - Heaviside step function - Hermite function - Heun functions - derivatives of Heun functions - generalized hypergeometric function - integer logarithms - imaginary part of a complex number - incomplete Bell polynomials - inverse Jacobi amplitude function - inverse Jacobi elliptic functions - Jacobi function - Jacobi amplitude function - Jacobi elliptic functions - Jacobi theta functions - Jacobi Zeta function - Kelvin functions - Kummer functions - Laguerre function - Lambert W function - associated Legendre function of the first kind - associated Legendre function of the second kind - Lerch's Phi function - logarithmic integral - natural logarithm (logarithm with base $ⅇ$ = 2.71...) - log-Gamma function - logarithm to arbitrary base - log to the base 10 - log to the base 2 - Lommel function s - Lommel function S - Mathieu characteristic function - Mathieu characteristic function - even general Mathieu function - first derivative of MathieuC - even $2\mathrm{\pi }$-periodic Mathieu function - first derivative of MathieuCE - Mathieu characteristic exponent - Floquet solution of Mathieu's equation - first derivative of MathieuFloquet - odd general Mathieu function - first derivative of MathieuS - odd $2\mathrm{\pi }$-periodic Mathieu function - first derivative of MathieuSE - MeijerG function - maximum of a sequence of real values - minimum of a sequence of real values - multiple polylogarithmic function - multiple zeta function - pochhammer symbol - polar representation of complex numbers - polylogarithm function - polygamma function - real part of a complex number - Riemann theta function - nearest integer to a number - sign of a real or complex number - hyperbolic sine integral - sine integral - spherical harmonic function - square root - shifted sine integral - Stirling number of the first kind - Stirling number of the second kind - Struve function - modified Struve function - non-principal root function - nearest integer to a number in the direction of 0 - unwinding number - Weber E function - Weierstrass P-function - Derivative of Weierstrass P-function - Weierstrass sigma-function - Weierstrass zeta-function - Whittaker functions - Wright omega function - Riemann and Hurwitz zeta functions

 • Additional mathematical functions are defined in various packages, such as the combinatorial functions package combinat, the number theory package NumberTheory, and the orthogonal polynomial package orthopoly. For a complete list of packages, see index[package].