Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ak9o)

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=-1/2, a₂>=-1/2

For fixed z and a₁=-1/2, a₂=1, a₃>=1

For fixed z and a₁=-1/2, a₂=1, a₃=3

For fixed z and a₁=-1/2, a₂=1, a₃=3, b₁=1/2

http://functions.wolfram.com/07.27.03.ak9o.01

Input Form

HypergeometricPFQ[{-(1/2), 1, 3}, {1/2, 7/2}, z] == -((5 I (-96 I - 88 I z + 180 I z^2 + 45 Pi^2 z^(5/2)))/(1536 z^2)) + (5 Sqrt[1 - z] (8 + 10 z + 15 z^2) ArcSin[Sqrt[z]])/(128 z^(5/2)) + (5 Sqrt[1 - z] (-160 - 294 z + 2 z^2 + 95 z^3 - 90 z^4 + 27 z^5) Log[1 - E^(I ArcSin[Sqrt[z]])])/(768 (-1 + z)^5) - (5 Sqrt[1 - z] (-160 - 294 z + 2 z^2 + 95 z^3 - 90 z^4 + 27 z^5) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (768 (-1 + z)^5) - (75/128) Sqrt[z] ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))] - (5 Sqrt[1 - z] (-160 - 294 z + 2 z^2 + 95 z^3 - 90 z^4 + 27 z^5) Log[1 + E^(I ArcSin[Sqrt[z]])])/(768 (-1 + z)^5) - (75/128) I Sqrt[z] PolyLog[2, -E^(I ArcSin[Sqrt[z]])] + (75/128) I Sqrt[z] PolyLog[2, E^(I ArcSin[Sqrt[z]])]

Standard Form

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MathML Form

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2 </cn> </apply> </apply> <apply> <ln /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </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> <plus /> 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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]