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

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=-1/2, a₃>=-1/2

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

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

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

Input Form

HypergeometricPFQ[{-(1/2), -(1/2), 1/2}, {5/2, 7/2}, z] == (15 Pi^2 (-1 - 4 z))/(1024 (-z)^(3/2)) + (5 Sqrt[1 - z] (-3 - 110 z + 128 z^2))/(2048 z^2) - (15 (-1 - 12 z + 24 z^2 - 16 z^3) Log[Sqrt[1 - z] + Sqrt[-z]])/ (2048 (-z)^(5/2)) - (45 (-1 - 4 z) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/ (512 (-z)^(3/2)) + (45 (-1 - 4 z) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/(256 (-z)^(3/2)) + (45 (-1 - 4 z) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/(256 (-z)^(3/2)) - (45 (-1 - 4 z) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/(256 (-z)^(3/2))

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <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> <apply> <power /> <apply> <times /> <cn type='integer'> 2048 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 45 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -4 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn 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/> <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> </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]