Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a841)

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=3/2

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

http://functions.wolfram.com/07.27.03.a841.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 3/2}, {1/2, 2}, -z] == (4 (15 + 1307 z - 6263 z^2 + 1917 z^3) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(735 Pi z) + (4 Sqrt[1 + z] (15 + 1307 z - 6263 z^2 + 1917 z^3) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(735 Pi z) - (16 Sqrt[1 + z] (-180 + 2003 z - 2238 z^2 + 315 z^3) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(735 Pi z) - (8 (375 - 2699 z - 1787 z^2 + 1287 z^3) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(735 Pi z)

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]