Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.6002)

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=1/2, a₃>=1/2

For fixed z and a₁=-7/2, a₂=1/2, a₃=3/2

For fixed z and a₁=-7/2, a₂=1/2, a₃=3/2, b₁=2

http://functions.wolfram.com/07.27.03.6002.01

Input Form

HypergeometricPFQ[{-(7/2), 1/2, 3/2}, {2, 4}, z] == (1/(4729725 Pi^2 z^3)) (256 (-3920 + 47285 z + 407260 z^2 + 189172 z^3 - 67994 z^4 + 17216 z^5 - 2048 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2) + (1/(4729725 Pi^2 z^3)) (256 Sqrt[1 - z] (3920 - 46305 z - 221305 z^2 - 14207 z^3 + 3936 z^4 - 512 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(4729725 Pi^2 z^3)) (256 (3920 - 47285 z - 407260 z^2 - 189172 z^3 + 67994 z^4 - 17216 z^5 + 2048 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(4729725 Pi^2 z^3)) (128 Sqrt[1 - z] (-3920 + 46305 z + 221305 z^2 + 14207 z^3 - 3936 z^4 + 512 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(4729725 Pi^2 z^3)) (128 (-3920 + 48265 z + 198520 z^2 + 96492 z^3 - 34507 z^4 + 8672 z^5 - 1024 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

Standard Form

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MathML Form

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type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 14207 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 221305 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 46305 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 3920 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <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 /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> 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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]