Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.4384)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=-3/2, a₃>=-3/2

For fixed z and a₁=-7/2, a₂=-3/2, a₃=3

For fixed z and a₁=-7/2, a₂=-3/2, a₃=3, b₁=5/2

http://functions.wolfram.com/07.27.03.4384.01

Input Form

HypergeometricPFQ[{-(7/2), -(3/2), 3}, {5/2, 7/2}, z] == (-1575 + 63945 z + 3628330 z^2 + 4177446 z^3 + 194985 z^4 - 10395 z^5)/ (5242880 z^2) - (21 (15 - 374 z + 10125 z^2 + 10200 z^3 - 18175 z^4 - 1890 z^5 + 99 z^6) Log[1 - Sqrt[z]])/(2097152 z^(5/2)) + (21 (15 - 374 z + 10125 z^2 + 10200 z^3 - 18175 z^4 - 1890 z^5 + 99 z^6) Log[1 + Sqrt[z]])/(2097152 z^(5/2)) - (315 (-2 + 45 z + 300 z^2 + 175 z^3) PolyLog[2, -Sqrt[z]])/ (262144 z^(3/2)) + (315 (-2 + 45 z + 300 z^2 + 175 z^3) PolyLog[2, Sqrt[z]])/(262144 z^(3/2))

Standard Form

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MathML Form

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</math>

Rule Form

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

2007-05-02

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]