Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.alq8)

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=-1/2, a₂>=-1/2

For fixed z and a₁=-1/2, a₂=3, a₃>=3

For fixed z and a₁=-1/2, a₂=3, a₃=3

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

http://functions.wolfram.com/07.27.03.alq8.01

Input Form

HypergeometricPFQ[{-(1/2), 3, 3}, {-(3/2), -(3/2)}, z] == (64 - 640 z + 768 z^2 - 79954 z^3 - 125441 z^4 - 20022 z^5)/ (64 (-1 + z)^8) - (315 (42 z^(5/2) + 369 z^(7/2) + 280 z^(9/2) + 24 z^(11/2)) ArcSin[Sqrt[z]])/(64 Sqrt[1 - z] (-1 + z)^8)

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]