Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ast0)

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=4, a₃>=4

For fixed z and a₁=3/2, a₂=4, a₃=4

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

http://functions.wolfram.com/07.27.03.ast0.01

Input Form

HypergeometricPFQ[{3/2, 4, 4}, {-(7/2), -(7/2)}, -z] == (1/(12544 (1 + z)^16)) (12544 + 176128 z + 1234944 z^2 + 3747840 z^3 + 492887040 z^4 - 126284933376 z^5 + 2816110297728 z^6 - 16690780645056 z^7 + 35349447031200 z^8 - 29369799338750 z^9 + 9392645425735 z^10 - 997022735280 z^11 + 22250968740 z^12) - (6435 (183040 z^(9/2) - 11406720 z^(11/2) + 135908160 z^(13/2) - 528167776 z^(15/2) + 800950650 z^(17/2) - 497069625 z^(19/2) + 120427450 z^(21/2) - 9523800 z^(23/2) + 144144 z^(25/2)) ArcSinh[Sqrt[z]])/(1792 Sqrt[1 + z] (1 + 16 z + 120 z^2 + 560 z^3 + 1820 z^4 + 4368 z^5 + 8008 z^6 + 11440 z^7 + 12870 z^8 + 11440 z^9 + 8008 z^10 + 4368 z^11 + 1820 z^12 + 560 z^13 + 120 z^14 + 16 z^15 + z^16))

Standard Form

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MathML Form

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type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1820 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 560 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 120 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> </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]