Generalized hypergeometric function 4F3: Specific values (formula 07.28.03.0075)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Specialized values

For fixed a₂, b₂, z

http://functions.wolfram.com/07.28.03.0075.01

Input Form

HypergeometricPFQ[{-n, a, a + 1/2, 2 a + n}, {2 a, f, 2 a - f + 1}, z] == (((-1)^n n!^2)/(Pochhammer[f, n] Pochhammer[2 a - f + 1, n])) JacobiP[n, f - 1, 2 a - f, Sqrt[1 - z]] JacobiP[n, f - 1, 2 a - f, -Sqrt[1 - 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]