Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ave9)

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=-5/2

http://functions.wolfram.com/07.27.03.ave9.01

Input Form

HypergeometricPFQ[{4, 4, 4}, {-(5/2), 1}, -z] == (1/(61440 (1 + z)^13)) (61440 + 2371584 z + 58007552 z^2 + 2139103232 z^3 - 35649512451 z^4 + 110996238360 z^5 - 107066462496 z^6 + 33935958792 z^7 - 3034127168 z^8 + 43686784 z^9) - (3003 (184041 z^(7/2) - 1349634 z^(9/2) + 2687100 z^(11/2) - 1829200 z^(13/2) + 422880 z^(15/2) - 27264 z^(17/2) + 256 z^(19/2)) ArcSinh[Sqrt[z]])/(4096 Sqrt[1 + z] (1 + 13 z + 78 z^2 + 286 z^3 + 715 z^4 + 1287 z^5 + 1716 z^6 + 1716 z^7 + 1287 z^8 + 715 z^9 + 286 z^10 + 78 z^11 + 13 z^12 + z^13))

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]