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

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=1, a₃>=1

For fixed z and a₁=-5/2, a₂=1, a₃=5/2

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

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

Input Form

HypergeometricPFQ[{-(5/2), 1, 5/2}, {7/2, 7/2}, z] == (-1285 + 1205 z + 887 z^2 - 355 z^3 + 60 z^4)/(2048 z^2) + (5 (-137 + 300 z - 300 z^2 + 200 z^3 - 75 z^4 + 12 z^5) Log[1 - Sqrt[z]])/ (4096 z^(5/2)) - (5 (-137 + 300 z - 300 z^2 + 200 z^3 - 75 z^4 + 12 z^5) Log[1 + Sqrt[z]])/(4096 z^(5/2)) - (75 PolyLog[2, -Sqrt[z]])/ (512 z^(5/2)) + (75 PolyLog[2, Sqrt[z]])/(512 z^(5/2))

Standard Form

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MathML Form

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</apply> <cn type='integer'> -137 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4096 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 75 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> 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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]