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

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=5/2

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

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

Input Form

HypergeometricPFQ[{5/2, 5/2, 5/2}, {-(1/2), 3}, z] == (16 (10 - 47 z + 84 z^2 - 27 z^3 + 108 z^4) EllipticE[z])/ (9 Pi (-1 + z)^5 z^2) + (32 (5 - 21 z + 33 z^2 - 9 z^3 + 24 z^4) EllipticK[z])/(9 Pi (-1 + z)^4 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]