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

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=3, a₃>=3

For fixed z and a₁=5/2, a₂=3, a₃=4

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

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

Input Form

HypergeometricPFQ[{5/2, 3, 4}, {-(7/2), -(7/2)}, z] == (1/(6272 (-1 + z)^16)) (6272 - 84992 z + 592896 z^2 - 1325056 z^3 + 383004160 z^4 + 102925605888 z^5 + 2393429491712 z^6 + 14946048616576 z^7 + 33846890198784 z^8 + 30766992639240 z^9 + 11195878722600 z^10 + 1462608582435 z^11 + 49603391838 z^12 + 72144072 z^13) + (6435 (146432 z^(9/2) + 9464832 z^(11/2) + 117885312 z^(13/2) + 484145920 z^(15/2) + 788338200 z^(17/2) + 538580328 z^(19/2) + 149977113 z^(21/2) + 14882868 z^(23/2) + 360360 z^(25/2)) ArcSin[Sqrt[z]])/(896 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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<cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4368 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </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'> -1 </cn> <apply> <times /> <cn type='integer'> 560 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </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'> -1 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> </apply> </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]