Special Functions

Bessel, Legendre, elliptic, error, gamma, and other functions

Special functions are a group of well-known mathematical functions that frequently arise in real-world applications. You can use them to calculate Bessel functions, beta functions, gamma functions, error functions, elliptic integrals, and more. Since the properties of these functions have been studied extensively, you can find more information about many of them in the NIST Digital Library of Mathematical Functions.

Several examples of plots of special functions, including Bessel, elliptic, and Legendre functions

Functions

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airyAiry Functions
besselhBessel function of third kind (Hankel function)
besseliModified Bessel function of first kind
besseljBessel function of first kind
besselkModified Bessel function of second kind
besselyBessel function of second kind
betaBeta function
betaincIncomplete beta function
betaincinvBeta inverse cumulative distribution function
betalnLogarithm of beta function
erfError function
erfcComplementary error function
erfcinvInverse complementary error function
erfcxScaled complementary error function
erfinvInverse error function
gammaGamma function
gammaincRegularized incomplete gamma function
gammaincinvInverse of regularized incomplete gamma function
gammalnLogarithm of gamma function
psiDigamma and polygamma functions
ellipjJacobi elliptic functions
ellipkeComplete elliptic integrals of first and second kind
expintExponential integral function
legendreAssociated Legendre functions