Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a7s9)

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=-5/2, a₃>=-5/2

For fixed z and a₁=-5/2, a₂=-5/2, a₃=-3/2

For fixed z and a₁=-5/2, a₂=-5/2, a₃=-3/2, b₁=-1/2

http://functions.wolfram.com/07.27.03.a7s9.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), -(3/2)}, {-(1/2), 5/2}, z] == (-(75/256)) Pi^2 (-z)^(3/2) - (Sqrt[1 - z] (-75 - 29218 z - 194984 z^2 + 17712 z^3))/(32768 z) + (15 (5 - 240 z - 4320 z^2 - 9600 z^3 + 384 z^4) Log[Sqrt[1 - z] + Sqrt[-z]])/(32768 (-z)^(3/2)) + (225/128) (-z)^(3/2) Log[Sqrt[1 - z] + Sqrt[-z]]^2 - (225/64) (-z)^(3/2) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]] - (225/64) (-z)^(3/2) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]] + (225/64) (-z)^(3/2) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]]

Standard Form

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MathML Form

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type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 225 <sep /> 64 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </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> <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]