Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2652)

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=1/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃=1/2, b₁=4

http://functions.wolfram.com/07.27.03.2652.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 1/2}, {4, 4}, z] == (1/(66958716825 Pi^2 z^3)) (2048 (-1663666 - 56484357 z - 447005786 z^2 + 611577259 z^3 + 140593668 z^4 + 9465449 z^5 + 23760 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2) - (1/(66958716825 Pi^2 z^3)) (2048 Sqrt[1 - z] (-1303306 - 40616506 z - 303777465 z^2 + 210360199 z^3 + 43085404 z^4 + 2336400 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) - (1/(66958716825 Pi^2 z^3)) (2048 (-1663666 - 56484357 z - 447005786 z^2 + 611577259 z^3 + 140593668 z^4 + 9465449 z^5 + 23760 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] (-1303306 - 40616506 z - 303777465 z^2 + 210360199 z^3 + 43085404 z^4 + 2336400 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(66958716825 Pi^2 z^3)) (1024 (-1303306 - 40054943 z - 287409523 z^2 + 588659899 z^3 + 81200027 z^4 + 5317567 z^5 + 11880 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]