Gauss hypergeometric function 2F1: Identities (formula 07.23.17.0053)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Identities

Functional identities

Division on even and odd parts and generalization

http://functions.wolfram.com/07.23.17.0053.01

Input Form

Hypergeometric2F1[a, b, c, z] == Sum[(z^k/k!) ((Pochhammer[a, k] Pochhammer[b, k])/Pochhammer[c, k]) HypergeometricPFQ[{1, (a + k)/n, \[Ellipsis], (a + k + n - 1)/n, (b + k)/n, \[Ellipsis], (b + k + n - 1)/n}, {(k + 1)/n, \[Ellipsis], (k + n)/n, (c + k)/n, \[Ellipsis], (c + k + n - 1)/n}, z^n], {k, 0, n - 1}]

Standard Form

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MathML Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]