Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.arj0)

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=3/2, a₃>=3/2

For fixed z and a₁=3/2, a₂=3/2, a₃=7/2

For fixed z and a₁=3/2, a₂=3/2, a₃=7/2, b₁=-5/2

http://functions.wolfram.com/07.27.03.arj0.01

Input Form

HypergeometricPFQ[{3/2, 3/2, 7/2}, {-(5/2), 3}, z] == -((32 (315 - 1785 z + 4140 z^2 - 4953 z^3 + 3051 z^4 - 256 z^5 + 128 z^6) EllipticE[z])/(75 Pi (-1 + z)^6 z^2)) + (16 (-630 + 3255 z - 6780 z^2 + 7131 z^3 - 3744 z^4 + 128 z^5) EllipticK[z])/(75 Pi (-1 + z)^5 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]