Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.av05)

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=-7/2

http://functions.wolfram.com/07.27.03.av05.01

Input Form

HypergeometricPFQ[{3, 7/2, 4}, {-(7/2), -(7/2)}, -z] == (1/(4480 (1 + z)^17)) (4480 + 60800 z + 458752 z^2 + 134144 z^3 + 707318272 z^4 - 222536742400 z^5 + 6123482859520 z^6 - 46455215709952 z^7 + 132413097022336 z^8 - 159352473872592 z^9 + 83008607527560 z^10 - 17802471691290 z^11 + 1345991437791 z^12 - 23897008278 z^13 + 10306296 z^14) + (1287 (-292864 z^(9/2) + 22031360 z^(11/2) - 326119680 z^(13/2) + 1635885440 z^(15/2) - 3376762480 z^(17/2) + 3085378296 z^(19/2) - 1249518270 z^(21/2) + 209508585 z^(23/2) - 12175020 z^(25/2) + 154440 z^(27/2)) ArcSinh[Sqrt[z]])/(128 Sqrt[1 + z] (1 + 17 z + 136 z^2 + 680 z^3 + 2380 z^4 + 6188 z^5 + 12376 z^6 + 19448 z^7 + 24310 z^8 + 24310 z^9 + 19448 z^10 + 12376 z^11 + 6188 z^12 + 2380 z^13 + 680 z^14 + 136 z^15 + 17 z^16 + z^17))

Standard Form

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MathML Form

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<cn type='integer'> 6188 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2380 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 680 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 136 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 17 </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]