Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.0307)

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=1

http://functions.wolfram.com/07.27.03.0307.01

Input Form

HypergeometricPFQ[{-(1/2), 5/2, 5/2}, {1, 2}, z] == (8/(27 Pi^2 (-1 + z)^2 z)) (2 (-1 + 63 z - 126 z^2 + 64 z^3) EllipticE[(1 - Sqrt[1 - z])/2]^2 + 2 (1 - 63 z + 126 z^2 - 64 z^3 + Sqrt[1 - z] (1 - 20 z + 16 z^2)) EllipticE[(1 - Sqrt[1 - z])/2] EllipticK[(1 - Sqrt[1 - z])/2] - (1 - 34 z + 65 z^2 - 32 z^3 + Sqrt[1 - z] (1 - 20 z + 16 z^2)) EllipticK[(1 - 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)

2001-10-29

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]