Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a844)

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.a844.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 3/2}, {1/2, 3}, z] == (16 (10 - 65 z + 2727 z^2 + 8653 z^3 + 1987 z^4) EllipticE[z])/ (6615 Pi z^2) + (32 (-5 + 35 z - 966 z^2 - 1166 z^3 + 1787 z^4 + 315 z^5) EllipticK[z])/(6615 Pi z^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]