Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.4516)

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=-7/2, a₂>=-7/2

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

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

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

http://functions.wolfram.com/07.27.03.4516.01

Input Form

HypergeometricPFQ[{-(7/2), -(3/2), 7/2}, {3, 4}, z] == -((1/(780404625 Pi^2 z^3)) (1024 (-3080 + 159723 z - 2202322 z^2 - 30808198 z^3 - 23903118 z^4 - 636800 z^5 + 30720 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2)) - (1/(780404625 Pi^2 z^3)) (2048 Sqrt[1 - z] (1540 - 56954 z + 767565 z^2 + 6743189 z^3 + 3887120 z^4 + 3840 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(780404625 Pi^2 z^3)) (1024 (-3080 + 159723 z - 2202322 z^2 - 30808198 z^3 - 23903118 z^4 - 636800 z^5 + 30720 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(780404625 Pi^2 z^3)) (1024 Sqrt[1 - z] (1540 - 56954 z + 767565 z^2 + 6743189 z^3 + 3887120 z^4 + 3840 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) - (1/(780404625 Pi^2 z^3)) (512 (-3080 + 115448 z - 1580534 z^2 - 18984250 z^3 - 13914059 z^4 - 319360 z^5 + 15360 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

Standard Form

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MathML Form

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<apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 780404625 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 512 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 15360 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 319360 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn 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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]