Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3091)

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=-7/2, a₂>=-7/2

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

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

For fixed z and a₁=-7/2, a₂=-5/2, a₃=5/2, b₁=1/2

http://functions.wolfram.com/07.27.03.3091.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 5/2}, {1/2, 3}, z] == (16 (-10 - 85 z + 14763 z^2 + 115457 z^3 + 70403 z^4 + 1200 z^5) EllipticE[z])/(31185 Pi z^2) + (32 (5 + 40 z - 5454 z^2 - 26104 z^3 + 17953 z^4 + 13560 z^5) EllipticK[z])/ (31185 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]