Hypergeometric Functions

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Hypergeometric Functions (218,254 formulas)



Hermite, Parabolic Cylinder, and Laguerre Functions

HermiteH[nu,z] (229 formulas)
ParabolicCylinderD[nu,z] (235 formulas)
LaguerreL[nu,z] (138 formulas)
LaguerreL[nu,lambda,z] (183 formulas)

Chebyshev and Fibonacci Functions

ChebyshevT[nu,z] (263 formulas)
ChebyshevU[nu,z] (238 formulas)
Fibonacci[nu,z] (141 formulas)

Legendre Functions

LegendreP[nu,z] (188 formulas)
LegendreP[nu,mu,z] (1 formula)
LegendreP[nu,mu,2,z] (284 formulas)
LegendreP[nu,mu,3,z] (315 formulas)
LegendreQ[nu,z] (103 formulas)
LegendreQ[nu,mu,z] (1 formula)
LegendreQ[nu,mu,2,z] (313 formulas)
LegendreQ[nu,mu,3,z] (366 formulas)

Gegenbauer and Jacobi Functions

GegenbauerC[nu,z] (205 formulas)
GegenbauerC[nu,lambda,z] (237 formulas)
JacobiP[nu,a,b,z] (185 formulas)

Confluent Hypergeometric Functions

Hypergeometric1F1[a,b,z] (750 formulas)
Hypergeometric1F1Regularized[a,b,z] (777 formulas)
HypergeometricU[a,b,z] (1017 formulas)
WhittakerM[nu,mu,z] (289 formulas)
WhittakerW[nu,mu,z] (181 formulas)

Hypergeometric Functions

HypergeometricPFQ[{},{},z] (18 formulas)
Hypergeometric0F1[b,z] (416 formulas)
Hypergeometric0F1Regularized[b,z] (409 formulas)
HypergeometricPFQ[{a},{},z] (42 formulas)
HypergeometricPFQ[{a1},{b1,b2},z] (21885 formulas)
Hypergeometric2F1[a,b,c,z] (111951 formulas)
Hypergeometric2F1Regularized[a,b,c,z] (865 formulas)
HypergeometricPFQ[{a1,a2},{b1,b2},z] (31337 formulas)
HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] (145 formulas)
HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] (40964 formulas)
HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] (360 formulas)
HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] (78 formulas)
HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] (15 formulas)
HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] (333 formulas)
HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] (310 formulas)

Meijer G Functions

MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] (1363 formulas)
MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z,r] (198 formulas)

Hypergeometric Functions of Several Variables

AppellF1[a,b1,b2,c,z1,z2] (102 formulas)

Angular Momentum Functions

SphericalHarmonicY[lambda,mu,theta,phi] (266 formulas)
ClebschGordan[{j1,m1},{j2,m2},{j,m}] (184 formulas)
ThreeJSymbol[{j1,m1},{j2,m2},{j3,m3}] (120 formulas)
SixJSymbol[{j1,j2,j3},{j4,j5,j6}] (254 formulas)

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