Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.auf2)

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=3, a₃>=3

For fixed z and a₁=5/2, a₂=3, a₃=4

For fixed z and a₁=5/2, a₂=3, a₃=4, b₁=-7/2

http://functions.wolfram.com/07.27.03.auf2.01

Input Form

HypergeometricPFQ[{5/2, 3, 4}, {-(7/2), 7/2}, z] == (1/(896 (-1 + z)^9 z^2)) (15360 - 135680 z + 530176 z^2 - 1197504 z^3 + 1697256 z^4 - 1435804 z^5 - 470559 z^6 - 2711950 z^7 - 120120 z^8) - (15 (1024 - 9728 z + 41344 z^2 - 103360 z^3 + 167960 z^4 - 184756 z^5 + 138567 z^6 + 84084 z^7 + 120120 z^8) ArcSin[Sqrt[z]])/ (896 Sqrt[1 - z] (-z^(5/2) + 9 z^(7/2) - 36 z^(9/2) + 84 z^(11/2) - 126 z^(13/2) + 126 z^(15/2) - 84 z^(17/2) + 36 z^(19/2) - 9 z^(21/2) + z^(23/2)))

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]