Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a8gn)

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=7/2

For fixed z and a₁=-5/2, a₂=-5/2, a₃=7/2, b₁=-3/2

http://functions.wolfram.com/07.27.03.a8gn.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 7/2}, {-(3/2), 4}, -z] == (1/(2401245 Pi z^3)) (32 (2520 - 4865 z + 19790 z^2 + 347247 z^3 + 938072 z^4 + 2013472 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2]) + (1/(2401245 Pi z^3)) (32 Sqrt[1 + z] (2520 - 4865 z + 19790 z^2 + 347247 z^3 + 938072 z^4 + 2013472 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) - (1/(2401245 Pi z^3)) (128 Sqrt[1 + z] (630 - 1295 z - 69900 z^2 - 206247 z^3 - 392488 z^4 + 443520 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) - (1/(2401245 Pi z^3)) (64 (1260 - 2275 z + 159590 z^2 + 759741 z^3 + 1723048 z^4 + 1126432 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])

Standard Form

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MathML Form

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/> <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'> 2401245 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </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]