Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.au2a)

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=5/2, a₂>=5/2

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

For fixed z and a₁=5/2, a₂=5/2, a₃=3

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

http://functions.wolfram.com/07.27.03.au2a.01

Input Form

HypergeometricPFQ[{5/2, 5/2, 3}, {1, 1}, -z] == ((41 - 320 z + 261 z^2 - 18 z^3) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(6 Pi (1 + z)^6) + ((41 - 320 z + 261 z^2 - 18 z^3) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(6 Pi (1 + z)^(11/2)) + ((-24 + 283 z - 306 z^2 + 27 z^3) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(6 Pi z (1 + z)^5) + ((24 - 341 z + 663 z^2 - 243 z^3 + 9 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (6 Pi z (1 + z)^(11/2))

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]