Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.6482)

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=7/2

For fixed z and a₁=-7/2, a₂=1/2, a₃=7/2, b₁=4

http://functions.wolfram.com/07.27.03.6482.01

Input Form

HypergeometricPFQ[{-(7/2), 1/2, 7/2}, {4, 4}, z] == -((1/(10145260125 Pi^2 z^3)) (2048 (-6907838 + 27396684 z - 81663988 z^2 - 55406965 z^3 + 22184640 z^4 - 5964800 z^5 + 737280 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2)) - (1/(10145260125 Pi^2 z^3)) (2048 Sqrt[1 - z] (4385318 - 16683247 z + 48530055 z^2 + 4583080 z^3 - 1358720 z^4 + 184320 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(10145260125 Pi^2 z^3)) (2048 (-6907838 + 27396684 z - 81663988 z^2 - 55406965 z^3 + 22184640 z^4 - 5964800 z^5 + 737280 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(10145260125 Pi^2 z^3)) (1024 Sqrt[1 - z] (4385318 - 16683247 z + 48530055 z^2 + 4583080 z^3 - 1358720 z^4 + 184320 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) - (1/(10145260125 Pi^2 z^3)) (1024 (-4385318 + 18245276 z - 54154814 z^2 - 28321165 z^3 + 11268640 z^4 - 3005440 z^5 + 368640 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

Standard Form

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MathML Form

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2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 10145260125 </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'> 2048 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 737280 </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'> 5964800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 22184640 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </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]