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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=4, a₃>=4

For fixed z and a₁=3/2, a₂=4, a₃=4

For fixed z and a₁=3/2, a₂=4, a₃=4, b₁=-5/2

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

Input Form

HypergeometricPFQ[{3/2, 4, 4}, {-(5/2), -(5/2)}, -z] == (1/(19200 (1 + z)^14)) (19200 + 195072 z + 1739008 z^2 - 157416448 z^3 + 33136663168 z^4 - 550760392448 z^5 + 2310538610912 z^6 - 3212304067232 z^7 + 1556978397117 z^8 - 234848056872 z^9 + 7128413292 z^10) - (3003 (-54912 z^(7/2) + 2635776 z^(9/2) - 23236512 z^(11/2) + 63239200 z^(13/2) - 61997975 z^(15/2) + 21905598 z^(17/2) - 2392104 z^(19/2) + 48048 z^(21/2)) ArcSinh[Sqrt[z]])/ (1280 Sqrt[1 + z] (1 + 14 z + 91 z^2 + 364 z^3 + 1001 z^4 + 2002 z^5 + 3003 z^6 + 3432 z^7 + 3003 z^8 + 2002 z^9 + 1001 z^10 + 364 z^11 + 91 z^12 + 14 z^13 + z^14))

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]