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

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.avax.01

Input Form

HypergeometricPFQ[{7/2, 4, 4}, {-(7/2), -(5/2)}, -z] == (1/(1280 (1 + z)^17)) (1280 + 13568 z + 157696 z^2 - 8968192 z^3 - 3613721600 z^4 + 347914158080 z^5 - 5293155066368 z^6 + 26175468654464 z^7 - 52170541112768 z^8 + 45218802445960 z^9 - 17009788507140 z^10 + 2568489040689 z^11 - 127196469972 z^12 + 1203858084 z^13) - (9009 (-732160 z^(9/2) + 25658880 z^(11/2) - 233697920 z^(13/2) + 801657920 z^(15/2) - 1187788056 z^(17/2) + 793652860 z^(19/2) - 234017355 z^(21/2) + 27683370 z^(23/2) - 1046760 z^(25/2) + 6864 z^(27/2)) ArcSinh[Sqrt[z]])/ (256 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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</ci> <cn type='integer'> 12 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12376 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 19448 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 24310 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 24310 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 19448 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12376 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <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> </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]