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

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=7/2, a₃>=7/2

For fixed z and a₁=2, a₂=7/2, a₃=4

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

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

Input Form

HypergeometricPFQ[{2, 7/2, 4}, {-(5/2), -(5/2)}, -z] == (1/(800 (1 + z)^14)) (800 + 7616 z + 76384 z^2 - 8744064 z^3 + 1886095904 z^4 - 32624306624 z^5 + 143931275488 z^6 - 213895638528 z^7 + 113930144328 z^8 - 19961382168 z^9 + 818296143 z^10 - 943740 z^11 + 8820 z^12) - (9009 (-3072 z^(7/2) + 152576 z^(9/2) - 1402752 z^(11/2) + 4026880 z^(13/2) - 4238520 z^(15/2) + 1657656 z^(17/2) - 213213 z^(19/2) + 6006 z^(21/2)) ArcSinh[Sqrt[z]])/ (160 Sqrt[1 + z] (1 + 14 z + 91 z^2 + 364 z^3 + 1001 z^4 + 2002 z^5 + 3003 z^6 + 3432 z^7 + 3003 z^8 + 2002 z^9 + 1001 z^10 + 364 z^11 + 91 z^12 + 14 z^13 + z^14))

Standard Form

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MathML Form

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<times /> <cn type='integer'> 3003 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2002 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1001 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 364 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 91 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 14 </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]