Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.aog6)

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=5/2, a₃>=5/2

For fixed z and a₁=1/2, a₂=5/2, a₃=5/2

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

http://functions.wolfram.com/07.27.03.aog6.01

Input Form

HypergeometricPFQ[{1/2, 5/2, 5/2}, {4, 4}, z] == -((2048 (334 + 13 z + 4 z^2) EllipticE[1/2 - Sqrt[1 - z]/2]^2)/ (225 Pi^2 z^3)) - (2048 Sqrt[1 - z] (-214 + z) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2])/ (225 Pi^2 z^3) + (2048 (334 + 13 z + 4 z^2) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2])/(225 Pi^2 z^3) + (1024 Sqrt[1 - z] (-214 + z) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/ (225 Pi^2 z^3) - (2048 (107 - 39 z + z^2) EllipticK[1/2 - Sqrt[1 - z]/2]^ 2)/(225 Pi^2 z^3)

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]