Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.auo0)

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=4, a₃>=4

For fixed z and a₁=5/2, a₂=4, a₃=4

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

http://functions.wolfram.com/07.27.03.auo0.01

Input Form

HypergeometricPFQ[{5/2, 4, 4}, {-(5/2), -(3/2)}, z] == (1/(2304 (-1 + z)^14)) (2304 - 7680 z + 1299200 z^2 - 328330240 z^3 - 20885038720 z^4 - 197874131840 z^5 - 560491471904 z^6 - 568101683864 z^7 - 208654249089 z^8 - 24268274184 z^9 - 568830108 z^10) - (5005 (54912 z^(7/2) + 1262976 z^(9/2) + 7074912 z^(11/2) + 13669000 z^(13/2) + 10056563 z^(15/2) + 2745270 z^(17/2) + 234696 z^(19/2) + 3696 z^(21/2)) ArcSin[Sqrt[z]])/ (256 Sqrt[1 - z] (1 - 14 z + 91 z^2 - 364 z^3 + 1001 z^4 - 2002 z^5 + 3003 z^6 - 3432 z^7 + 3003 z^8 - 2002 z^9 + 1001 z^10 - 364 z^11 + 91 z^12 - 14 z^13 + z^14))

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 1001 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 364 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 91 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 14 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]