Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ab33)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=1, a₃>=1

For fixed z and a₁=-5/2, a₂=1, a₃=1

For fixed z and a₁=-5/2, a₂=1, a₃=1, b₁=4

http://functions.wolfram.com/07.27.03.ab33.01

Input Form

HypergeometricPFQ[{-(5/2), 1, 1}, {4, 4}, z] == (2 (-58994 - 282577 z + 48640 z^2 - 7424 z^3 + 640 z^4))/(266805 z^2) - (4 (1 - Sqrt[1 - z]) (-72854 - 422021 z - 201728 z^2 + 24320 z^3 - 3712 z^4 + 320 z^5))/(266805 z^3) + (4 (8 + 88 z + 99 z^2) Log[(1/2) (1 + Sqrt[1 - z])])/(77 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]