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

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=4, a₃>=4

For fixed z and a₁=7/2, a₂=4, a₃=4

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

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

Input Form

HypergeometricPFQ[{7/2, 4, 4}, {-(7/2), -(7/2)}, -z] == (1/(1792 (1 + z)^18)) (1792 + 24064 z + 200448 z^2 - 626688 z^3 + 659966976 z^4 - 239195086848 z^5 + 7681383696384 z^6 - 69451340062464 z^7 + 242476640938368 z^8 - 371034853541456 z^9 + 259381959985720 z^10 - 81254841203250 z^11 + 10442125832853 z^12 - 446472919464 z^13 + 3673412028 z^14) - (6435 (292864 z^(9/2) - 25359360 z^(11/2) + 439522560 z^(13/2) - 2638100608 z^(15/2) + 6704528880 z^(17/2) - 7843707144 z^(19/2) + 4306051750 z^(21/2) - 1071459675 z^(23/2) + 108965142 z^(25/2) - 3586440 z^(27/2) + 20592 z^(29/2)) ArcSinh[Sqrt[z]])/ (256 Sqrt[1 + z] (1 + 18 z + 153 z^2 + 816 z^3 + 3060 z^4 + 8568 z^5 + 18564 z^6 + 31824 z^7 + 43758 z^8 + 48620 z^9 + 43758 z^10 + 31824 z^11 + 18564 z^12 + 8568 z^13 + 3060 z^14 + 816 z^15 + 153 z^16 + 18 z^17 + z^18))

Standard Form

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MathML Form

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type='integer'> 43758 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 48620 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 43758 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 31824 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 18564 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8568 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3060 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 816 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 153 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 18 </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]