Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.av8r)

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=7/2, a₃>=7/2

For fixed z and a₁=7/2, a₂=7/2, a₃=4

For fixed z and a₁=7/2, a₂=7/2, a₃=4, b₁=-5/2

http://functions.wolfram.com/07.27.03.av8r.01

Input Form

HypergeometricPFQ[{7/2, 7/2, 4}, {-(5/2), -(3/2)}, z] == (1/(15 (1 - z)^4 (-1 + z)^11)) (-15 + 29 z - 11865 z^2 + 3386355 z^3 + 266284970 z^4 + 3182644290 z^5 + 11863334574 z^6 + 16867766630 z^7 + 9637306965 z^8 + 2112295185 z^9 + 149143995 z^10 + 2081079 z^11)

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]