Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.0149)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

Specialized values

For fixed b, z

http://functions.wolfram.com/07.23.03.0149.01

Input Form

Hypergeometric2F1[-n, b, -2 n - 1, z] == ((((-1)^n n! Gamma[1 - b])/(1 + 2 n)!) (1/z)^((b + n)/2) z^((b + 3 n)/2) ((1 + b + 2 n) Sqrt[-1 + z] LegendreP[n, b + n, 2, (-2 + z)/z] + Sqrt[1/z] Sqrt[z] LegendreP[n, 1 + b + n, 2, (-2 + z)/z]))/ (-1 + z)^((b + n + 1)/2) /; Element[n, Integers] && n >= 0

Standard Form

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MathML Form

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Rule 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]