Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.auu2)

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=3, a₂>=3

For fixed z and a₁=3, a₂=3, a₃>=3

For fixed z and a₁=3, a₂=3, a₃=7/2

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

http://functions.wolfram.com/07.27.03.auu2.01

Input Form

HypergeometricPFQ[{3, 3, 7/2}, {-(1/2), 1/2}, -z] == (64 + 8640 z - 265152 z^2 + 1005872 z^3 - 855576 z^4 + 158793 z^5 - 3326 z^6)/(64 (1 + z)^9) + (1/(64 (1 + z)^(19/2))) (105 (-448 z^(3/2) + 4816 z^(5/2) - 10312 z^(7/2) + 5615 z^(9/2) - 680 z^(11/2) + 8 z^(13/2)) ArcSinh[Sqrt[z]])

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]