Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.auy2)

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, a₂>=3

For fixed z and a₁=3, a₂=7/2, a₃>=7/2

For fixed z and a₁=3, a₂=7/2, a₃=7/2

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

http://functions.wolfram.com/07.27.03.auy2.01

Input Form

HypergeometricPFQ[{3, 7/2, 7/2}, {-(5/2), -(3/2)}, z] == (1/(5 (1 - z)^3 (-1 + z)^11)) (-5 + 21 z - 2415 z^2 + 568015 z^3 + 37391550 z^4 + 365112930 z^5 + 1074739666 z^6 + 1149406830 z^7 + 458152695 z^8 + 61486425 z^9 + 2013165 z^10 + 4851 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]