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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=3, a₃>=3

For fixed z and a₁=3/2, a₂=3, a₃=4

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

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

Input Form

HypergeometricPFQ[{3/2, 3, 4}, {-(7/2), 5/2}, z] == -((1/(4480 (-1 + z)^9 z)) (3 (-1280 + 12800 z - 60768 z^2 + 190832 z^3 - 506878 z^4 + 2094477 z^5 + 2059602 z^6 + 40040 z^7))) - (3 (256 - 2432 z + 10336 z^2 - 25840 z^3 + 41990 z^4 - 46189 z^5 + 571428 z^6 + 216216 z^7) ArcSin[Sqrt[z]])/ (896 Sqrt[1 - z] (-z^(3/2) + 9 z^(5/2) - 36 z^(7/2) + 84 z^(9/2) - 126 z^(11/2) + 126 z^(13/2) - 84 z^(15/2) + 36 z^(17/2) - 9 z^(19/2) + z^(21/2)))

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]