Wolfram Mathematica Online Integrator

`LegendreP[n, x]`	Legendre polynomial
`LegendreP[n, m, x]`	associated Legendre polynomial
`GegenbauerC[n, m, x]`	Gegenbauer polynomial
`GegenbauerC[n, x]`	renormalized Gegenbauer polynomial
`SphericalHarmonicY[l, m, theta, phi]`	spherical harmonic
`ChebyshevT[n, x]`	Chebyshev polynomial of the first kind
`ChebyshevU[n, x]`	Chebyshev polynomial of the second kind
`HermiteH[n, x]`	Hermite polynomial
`LaguerreL[n, x]`	Laguerre polynomial
`LaguerreL[n, a, x]`	associated Laguerre polynomial
`JacobiP[n, a, b, x]`	Jacobi polynomial

Gamma and Related Functions

`Beta[a, b]`	beta function
`Beta[x, a, b]`	incomplete beta function
`BetaRegularized[x, a, b]`	regularized incomplete beta function
`Gamma[x]`	gamma function
`Gamma[a, x]`	incomplete gamma function
`Gamma[a, x₀, x₁]`	generalized incomplete gamma function
`GammaRegularized[a, x]`	regularized incomplete gamma function
`InverseBetaRegularized[x, a, b]`	inverse regularized beta function
`InverseGammaRegularized[a, x]`	inverse regularized gamma function
`Pochhammer[a, n]`	Pochhammer symbol
`PolyGamma[x]`	digamma function
`PolyGamma[n, x]`	nth derivative of the digamma function

Zeta and Related Functions

`LerchPhi[x, s, a]`	Lerch's transcendent
`PolyLog[n, x]`	polylogarithm function
`PolyLog[n, p, x]`	Nielsen generalized polylogarithm function
`RiemannSiegelTheta[x]`	Riemann-Siegel theta function
`RiemannSiegelZ[x]`	Riemann-Siegel Z function
`Zeta[x]`	Riemann zeta function
`Zeta[x, a]`	generalized Riemann zeta function

Exponential Integral and Related Functions

Error Function and Related Functions

`Erf[x]`	error function
`Erf[x0, x1]`	generalized error function
`Erfc[x]`	complementary error function
`Erfi[x]`	imaginary error function
`FresnelC[x]`, `FresnelS[x]`	Fresnel integrals
`InverseErf[x]`	inverse error function
`InverseErfc[x]`	inverse complementary error function

Bessel Functions

`AiryAi[x]`, `AiryBi[x]`	Airy functions
`AiryAiPrime[x]`, `AiryBiPrime[x]`	derivatives of Airy functions
`BesselJ[n, x]`	Bessel function of the first kind
`BesselY[n, x]`	Bessel function of the second kind
`BesselI[n, x]`	modified Bessel function of the first kind
`BesselK[n, x]`	modified Bessel function of the second kind
`StruveH[n, x]`	Struve function
`StruveL[n, x]`	modified Struve function

Legendre and Related Functions

`LegendreP[n, x]`	Legendre function of the first kind
`LegendreP[n, m, x]`	associated Legendre function of the first kind
`LegendreQ[n, x]`	Legendre function of the second kind
`LegendreQ[n, m, x]`	associated Legendre function of the second kind
`LegendreP[n, m, a, x]`, `LegendreQ[n, m, a, x]`	Legendre function of type a

Confluent Hypergeometric Functions

`Hypergeometric0F1[a, x]`	hypergeometric function
`Hypergeometric0F1Regularized[a, x]`	regularized hypergeometric function
`Hypergeometric1F1[a, b, x]`	Kummer confluent hypergeometric function
`Hypergeometric1F1Regularized[a, b, x]`	regularized confluent hypergeometric function
`HypergeometricU[a, b, x]`	confluent hypergeometric function of the second kind

Hypergeometric Functions and Generalizations

`Hypergeometric2F1[a, b, c, x]`	hypergeometric function
`Hypergeometric2F1Regularized[a, b, c, x]`	regularized hypergeometric function
`HypergeometricPFQ[{a₁, ... , a_p}, {b₁, ... , b_q}, x]`	generalized hypergeometric function
`HypergeometricPFQRegularized[{a₁, ... , a_p}, {b₁, ... , b_q}, x]`	regularized generalized hypergeometric function
`MeijerG[{{a₁, ... , a_n}, {a_n+1, ... , a_p}}, {{b₁, ... , b_m}, {b_m+1, ... , b_q}}, x]`	Meijer G-function
`AppelF1[a, b₁, b₂, c, x, y]`	Appell hypergeometric function of two variables

ProductLog Function

`ProductLog[x]`	Lambert W-function
`ProductLog[k, x]`	multiple values of the Lambert W-function

Elliptic Integrals

`EllipticK[x]`	complete elliptic integral of the first kind
`EllipticF[x, m]`	elliptic integral of the first kind
`EllipticE[x]`	complete elliptic integral of the second kind
`EllipticE[x, m]`	elliptic integral of the second kind
`EllipticPi[n, m]`	complete elliptic integral of the third kind
`EllipticPi[n, x, m]`	elliptic integral of the third kind
`JacobiZeta[x, m]`	Jacobi zeta function

Elliptic Functions

`JacobiAmplitude[x, m]`	Jacobi amplitude function
`JacobiCD[x, m]`, `JacobiCN[x, m]`, `JacobiCS[x, m]`, `JacobiDC[x, m]`, `JacobiDN[x, m]`, `JacobiDS[x, m]`, `JacobiNC[x, m]`, `JacobiND[x, m]`, `JacobiNS[x, m]`, `JacobiSC[x, m]`, `JacobiSD[x, m]`, `JacobiSN[x, m]`	Jacobi elliptic functions
`InverseJacobiCD[x, m]`, `InverseJacobiCN[x, m]`, `InverseJacobiCS[x, m]`, `InverseJacobiDC[x, m]`, `InverseJacobiDN[x, m]`, `InverseJacobiDS[x, m]`, `InverseJacobiNC[x, m]`, `InverseJacobiND[x, m]`, `InverseJacobiNS[x, m]`, `InverseJacobiSC[x, m]`, `InverseJacobiSD[x, m]`, `InverseJacobiSN[x, m]`	inverse Jacobi elliptic functions
`EllipticTheta[a, x, q]`	theta function
`EllipticThetaPrime[a, x, q]`	derivative of theta function
`WeierstrassP[x, {g₂, g₃}]`	Weierstrass elliptic function
`WeierstrassPPrime[x, {g₂, g₃}]`	derivative of Weierstrass elliptic function
`InverseWeierstrassP[x, {g₂, g₃}]`	inverse Weierstrass elliptic function
`WeierstrassSigma[x, {g₂, g₃}]`	Weierstrass sigma function
`WeierstrassZeta[z, {g₂, g₃}]`	Weierstrass zeta function

Mathieu and Related Functions

`MathieuC[a, q, x]`	even Mathieu function
`MathieuS[b, q, x]`	odd Mathieu function
`MathieuCPrime[a, q, x]`	derivative of even Mathieu function
`MathieuSPrime[b, q, x]`	derivative of odd Mathieu function

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