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

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=5/2, a₃>=5/2

For fixed z and a₁=-3/2, a₂=5/2, a₃=3

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

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

Input Form

HypergeometricPFQ[{-(3/2), 5/2, 3}, {1, 1}, -z] == ((41 + 338 z + 580 z^2 + 280 z^3) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(6 Pi (1 + z)^2) + ((41 + 338 z + 580 z^2 + 280 z^3) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(6 Pi (1 + z)^(3/2)) + ((-24 - 341 z - 880 z^2 - 560 z^3) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(6 Pi z (1 + z)) + ((24 + 283 z + 545 z^2 + 280 z^3) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(6 Pi z (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]