Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1301)

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=-7/2, a₃>=-7/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃=-1/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃=-1/2, b₁=5/2

http://functions.wolfram.com/07.27.03.1301.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), -(1/2)}, {5/2, 5/2}, z] == (147 (-Pi^2 - 100 Pi^2 z + 800 Pi^2 z^2))/(2097152 (-z)^(3/2)) - (Sqrt[1 - z] (66885 - 20476010 z + 10288536 z^2 + 1262808 z^3 + 43136 z^4))/ (26214400 z) - (21 (427 + 33250 z + 112000 z^2 - 56000 z^3 - 5600 z^4 - 128 z^5) Log[Sqrt[1 - z] + Sqrt[-z]])/(5242880 (-z)^(3/2)) - (441 (-1 - 100 z + 800 z^2) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/ (1048576 (-z)^(3/2)) + (441 (-1 - 100 z + 800 z^2) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/ (524288 (-z)^(3/2)) + (441 (-1 - 100 z + 800 z^2) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/(524288 (-z)^(3/2)) - (441 (-1 - 100 z + 800 z^2) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/ (524288 (-z)^(3/2))

Standard Form

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MathML Form

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type='integer'> 100 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <ln /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1048576 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 21 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -128 </cn> <apply> <power /> <ci> z </ci> <cn 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</ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10288536 </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'> 20476010 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 66885 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 26214400 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 441 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 800 </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'> 100 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 524288 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 441 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 800 </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'> 100 </cn> <ci> z </ci> 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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]