Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.0034)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Values at z=1

For fixed a₂, a₃

http://functions.wolfram.com/07.27.03.0034.01

Input Form

HypergeometricPFQ[{1, b, c}, {m - b, m - c}, 1] == (-(1/2)) Sum[(Pochhammer[1 + b - m, k] Pochhammer[1 + c - m, k])/ (Pochhammer[1 - b, k] Pochhammer[1 - c, k]), {k, 1, m - 2}] + ((Sqrt[Pi] Pochhammer[m - 2 b, m] Pochhammer[m - 2 c, m] Pochhammer[m - b - c, m])/(2^(2 m + 1) Pochhammer[m - b - c - 1/2, m])) ((Gamma[1 - b] Gamma[1 - c] Gamma[2 m - b - c - 1/2])/ (Gamma[1/2 - b + m] Gamma[1/2 - c + m] Gamma[2 m - b - c])) /; Re[b + c] < m - 1/2 && Element[m - 2, Integers] && m - 2 >= 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,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]