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

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=3/2

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

Input Form

HypergeometricPFQ[{-(3/2), -(3/2), 7/2}, {3/2, 3}, z] == (32 (1 + 37 z + 2823 z^2 + 2283 z^3) EllipticE[z])/(18375 Pi z^2) + (16 (-2 - 73 z - 3312 z^2 + 1707 z^3 + 1680 z^4) EllipticK[z])/ (18375 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]