Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.8210)

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=2, a₃>=2

For fixed z and a₁=-7/2, a₂=2, a₃=2

For fixed z and a₁=-7/2, a₂=2, a₃=2, b₁=4

http://functions.wolfram.com/07.27.03.8210.01

Input Form

HypergeometricPFQ[{-(7/2), 2, 2}, {4, 4}, z] == -((16 (307231 + 147844 z - 313796 z^2 + 218460 z^3 - 77140 z^4 + 11340 z^5))/ (6441435 z^2)) + (1/(6441435 z^3)) (32 (1 - Sqrt[1 - z]) (397321 + 375090 z + 73922 z^2 - 156898 z^3 + 109230 z^4 - 38570 z^5 + 5670 z^6)) + (32 (4 + 13 z) Log[(1/2) (1 + Sqrt[1 - z])])/(143 z^3)

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)

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]