Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3388)

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=-5/2, a₃>=-5/2

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

For fixed z and a₁=-7/2, a₂=-5/2, a₃=7/2, b₁=4

http://functions.wolfram.com/07.27.03.3388.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 7/2}, {4, 4}, z] == (1/(66958716825 Pi^2 z^3)) (2048 (1111114 - 10123899 z + 97904462 z^2 + 1355784137 z^3 + 1503229227 z^4 + 273632080 z^5 + 1520640 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2) - (1/(66958716825 Pi^2 z^3)) (2048 Sqrt[1 - z] (750754 - 6805583 z + 67156080 z^2 + 603746237 z^3 + 535642460 z^4 + 74574720 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) - (1/(66958716825 Pi^2 z^3)) (2048 (1111114 - 10123899 z + 97904462 z^2 + 1355784137 z^3 + 1503229227 z^4 + 273632080 z^5 + 1520640 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(66958716825 Pi^2 z^3)) (1024 Sqrt[1 - z] (750754 - 6805583 z + 67156080 z^2 + 603746237 z^3 + 535642460 z^4 + 74574720 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(66958716825 Pi^2 z^3)) (1024 (750754 - 7090870 z + 69719908 z^2 + 839492255 z^3 + 888853486 z^4 + 155507240 z^5 + 760320 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

Standard Form

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MathML Form

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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]