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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=3/2, a₃>=3/2

For fixed z and a₁=3/2, a₂=3/2, a₃=5/2

For fixed z and a₁=3/2, a₂=3/2, a₃=5/2, b₁=-1/2

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

Input Form

HypergeometricPFQ[{3/2, 3/2, 5/2}, {-(1/2), 4}, -z] == -((32 (280 + 535 z + 257 z^2 + 8 z^3) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(3 Pi z^3 (1 + z)^2)) - (32 (280 + 535 z + 257 z^2 + 8 z^3) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(3 Pi z^3 (1 + z)^(3/2)) + (64 (140 + 145 z + 8 z^2) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(3 Pi z^3 (1 + z)) + (128 (70 + 125 z + 52 z^2) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(3 Pi z^3 (1 + z)^(3/2))

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]