Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ae9o)

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=7/2

For fixed z and a₁=-3/2, a₂=-3/2, a₃=7/2, b₁=-7/2

http://functions.wolfram.com/07.27.03.ae9o.01

Input Form

HypergeometricPFQ[{-(3/2), -(3/2), 7/2}, {-(7/2), 4}, -z] == (32 (1144 - 1177 z + 1872 z^2 + 4928 z^3 + 1024 z^4) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(55125 Pi z^3) + (32 Sqrt[1 + z] (1144 - 1177 z + 1872 z^2 + 4928 z^3 + 1024 z^4) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(55125 Pi z^3) + (256 Sqrt[1 + z] (-143 + 165 z + 600 z^2 + 128 z^3) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(55125 Pi z^3) - (64 (572 - 517 z + 4272 z^2 + 5440 z^3 + 1024 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(55125 Pi z^3)

Standard Form

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MathML Form

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</semantics> </math>

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]