Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.av0r)

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=7/2, a₃>=7/2

For fixed z and a₁=3, a₂=7/2, a₃=4

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

http://functions.wolfram.com/07.27.03.av0r.01

Input Form

HypergeometricPFQ[{3, 7/2, 4}, {-(5/2), -(3/2)}, -z] == (1/(640 (1 + z)^14)) (640 + 1792 z + 387968 z^2 + 100219392 z^3 - 6487306112 z^4 + 62757199232 z^5 - 182482203904 z^6 + 191542672464 z^7 - 74033643684 z^8 + 9386028729 z^9 - 267824634 z^10 + 194040 z^11) + (9009 (-16896 z^(7/2) + 395648 z^(9/2) - 2265216 z^(11/2) + 4499440 z^(13/2) - 3436620 z^(15/2) + 991683 z^(17/2) - 93324 z^(19/2) + 1848 z^(21/2)) ArcSinh[Sqrt[z]])/(128 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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type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 364 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </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'> 14 </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]