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

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=4, a₂>=4

For fixed z and a₁=4, a₂=4, a₃>=4

For fixed z and a₁=4, a₂=4, a₃=4

For fixed z and a₁=4, a₂=4, a₃=4, b₁=-3/2

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

Input Form

HypergeometricPFQ[{4, 4, 4}, {-(3/2), 3}, z] == (4608 - 111616 z + 2910720 z^2 + 26195755 z^3 + 34109440 z^4 + 9273432 z^5 + 365336 z^6)/(4608 (-1 + z)^10) + (385 (2541 z^(5/2) + 9570 z^(7/2) + 7524 z^(9/2) + 1328 z^(11/2) + 32 z^(13/2)) ArcSin[Sqrt[z]])/(512 Sqrt[1 - z] (-1 + z)^10)

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]