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Gamma, Beta, Erf (5,032 formulas)



Factorials

Factorial[n] (153 formulas)
Factorial2[n] (77 formulas)
Pochhammer[a,n] (103 formulas)

Binomials

Binomial[n,k] (147 formulas)
Multinomial[n1,n2,...,nm] (32 formulas)
CatalanNumber[n] (102 formulas)

Gamma Functions and Inverses

Gamma[z] (193 formulas)
Gamma[a,z] (153 formulas)
Gamma[a,z1,z2] (90 formulas)
GammaRegularized[a,z] (142 formulas)
GammaRegularized[a,z1,z2] (85 formulas)
Subfactorial[z] (91 formulas)
LogGamma[z] (130 formulas)
InverseGammaRegularized[a,z] (29 formulas)
InverseGammaRegularized[a,z1,z2] (17 formulas)

Differentiated Gamma Functions

PolyGamma[z] (117 formulas)
PolyGamma[nu,z] (214 formulas)
HarmonicNumber[z] (127 formulas)
HarmonicNumber[z,r] (92 formulas)

Beta Functions and Inverses

Beta[a,b] (72 formulas)
Beta[z,a,b] (193 formulas)
Beta[z1,z2,a,b] (106 formulas)
BetaRegularized[z,a,b] (173 formulas)
BetaRegularized[z1,z2,a,b] (98 formulas)
InverseBetaRegularized[z,a,b] (31 formulas)
InverseBetaRegularized[z1,z2,a,b] (15 formulas)

Probability Integrals and Inverses

Erf[z] (239 formulas)
Erf[z1,z2] (54 formulas)
Erfc[z] (235 formulas)
Erfi[z] (246 formulas)
InverseErf[z] (23 formulas)
InverseErf[z1,z2] (20 formulas)
InverseErfc[z] (24 formulas)

Fresnel Integrals

FresnelS[z] (108 formulas)
FresnelC[z] (226 formulas)

Exponential Integrals

ExpIntegralE[nu,z] (133 formulas)
ExpIntegralEi[z] (183 formulas)
LogIntegral[z] (90 formulas)
SinIntegral[z] (166 formulas)
CosIntegral[z] (174 formulas)
SinhIntegral[z] (159 formulas)
CoshIntegral[z] (170 formulas)