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

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=3/2, a₃>=3/2

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

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

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

Input Form

HypergeometricPFQ[{-(5/2), 3/2, 3/2}, {-(1/2), 3}, -z] == -((32 (25 + 5 z - 11 z^2 + 64 z^3 + 64 z^4) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(105 Pi z^2)) - (32 Sqrt[1 + z] (25 + 5 z - 11 z^2 + 64 z^3 + 64 z^4) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(105 Pi z^2) - (32 Sqrt[1 + z] (-25 - 15 z + 56 z^2 + 64 z^3) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(105 Pi z^2) + (32 (25 - 5 z + 34 z^2 + 192 z^3 + 128 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(105 Pi z^2)

Standard Form

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MathML Form

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type='integer'> 5 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 25 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 105 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 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]