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

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=-7/2

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

Input Form

HypergeometricPFQ[{5/2, 4, 4}, {-(7/2), -(7/2)}, -z] == (1/(12544 (1 + z)^17)) (12544 + 172288 z + 1296384 z^2 + 952320 z^3 + 1778519040 z^4 - 553433266176 z^5 + 15051627967488 z^6 - 112579709698176 z^7 + 315264173579520 z^8 - 370795806516200 z^9 + 187163046258760 z^10 - 38294677232955 z^11 + 2669644957980 z^12 - 39249270060 z^13) + (6435 (-732160 z^(9/2) + 54512640 z^(11/2) - 797086080 z^(13/2) + 3939152896 z^(15/2) - 7980509880 z^(17/2) + 7115963400 z^(19/2) - 2786008225 z^(21/2) + 443821950 z^(23/2) - 23567544 z^(25/2) + 240240 z^(27/2)) ArcSinh[Sqrt[z]])/ (1792 Sqrt[1 + z] (1 + 17 z + 136 z^2 + 680 z^3 + 2380 z^4 + 6188 z^5 + 12376 z^6 + 19448 z^7 + 24310 z^8 + 24310 z^9 + 19448 z^10 + 12376 z^11 + 6188 z^12 + 2380 z^13 + 680 z^14 + 136 z^15 + 17 z^16 + z^17))

Standard Form

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MathML Form

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type='integer'> 12376 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 19448 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 24310 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 24310 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 19448 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12376 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6188 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2380 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 680 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 136 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 17 </cn> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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]