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

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=2, a₂>=2

For fixed z and a₁=2, a₂=3, a₃>=3

For fixed z and a₁=2, a₂=3, a₃=7/2

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

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

Input Form

HypergeometricPFQ[{2, 3, 7/2}, {-(7/2), -(7/2)}, -z] == (1/(2800 (1 + z)^15)) (2800 + 37200 z + 242736 z^2 + 743120 z^3 + 64640880 z^4 - 14626389360 z^5 + 286301732080 z^6 - 1460735932656 z^7 + 2594260365840 z^8 - 1740461168160 z^9 + 423304441560 z^10 - 30485480850 z^11 + 325007463 z^12 + 228690 z^13) - (1287 (22528 z^(9/2) - 1248256 z^(11/2) + 13022464 z^(13/2) - 43435392 z^(15/2) + 55014960 z^(17/2) - 27411384 z^(19/2) + 5002998 z^(21/2) - 262977 z^(23/2) + 1716 z^(25/2)) ArcSinh[Sqrt[z]])/ (80 Sqrt[1 + z] (1 + 15 z + 105 z^2 + 455 z^3 + 1365 z^4 + 3003 z^5 + 5005 z^6 + 6435 z^7 + 6435 z^8 + 5005 z^9 + 3003 z^10 + 1365 z^11 + 455 z^12 + 105 z^13 + 15 z^14 + z^15))

Standard Form

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MathML Form

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type='integer'> 1365 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 455 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 105 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 15 </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]