Generalized hypergeometric function 4F3: Specific values (formula 07.28.03.0079)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]

Specific values

Specialized values

For fixed z and integer parameters

http://functions.wolfram.com/07.28.03.0079.01

Input Form

HypergeometricPFQ[{-n, -n, -n, 1/2 - n}, {3/2, -2 n, -(1/2) - 2 n}, z] == (((2 n)! n!^2 2^(2 n) z^n)/(4 n + 1)!) LegendreP[2 n + 1, (Sqrt[1 - z] + 1)/Sqrt[-z]] LegendreP[2 n + 1, (Sqrt[1 - z] - 1)/Sqrt[-z]] /; 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},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,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]