Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.7264)

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=1, a₃>=1

For fixed z and a₁=-7/2, a₂=1, a₃=3

For fixed z and a₁=-7/2, a₂=1, a₃=3, b₁=4

http://functions.wolfram.com/07.27.03.7264.01

Input Form

HypergeometricPFQ[{-(7/2), 1, 3}, {4, 4}, z] == (-1048744 + 1600827 z + 4374560 z^2 - 2478560 z^3 + 796320 z^4 - 110880 z^5)/ (6441435 z^2) + (1/(6441435 z^3)) (32 (1 - Sqrt[1 - z]) (88069 - 113623 z + 151269 z^2 - 136705 z^3 + 77455 z^4 - 24885 z^5 + 3465 z^6)) + (32 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]