Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.aqk7)

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=1, a₂>=1

For fixed z and a₁=1, a₂=5/2, a₃>=5/2

For fixed z and a₁=1, a₂=5/2, a₃=3

For fixed z and a₁=1, a₂=5/2, a₃=3, b₁=-7/2

http://functions.wolfram.com/07.27.03.aqk7.01

Input Form

HypergeometricPFQ[{1, 5/2, 3}, {-(7/2), -(7/2)}, -z] == (1/(1960 (1 + z)^13)) (1960 + 24280 z + 139968 z^2 + 475024 z^3 + 4466584 z^4 - 553176312 z^5 + 7268598480 z^6 - 22690420896 z^7 + 21541672152 z^8 - 6118960848 z^9 + 384298824 z^10 - 628425 z^11 + 13230 z^12) - (1287 (1024 z^(9/2) - 39936 z^(11/2) + 274560 z^(13/2) - 549120 z^(15/2) + 360360 z^(17/2) - 72072 z^(19/2) + 3003 z^(21/2)) ArcSinh[Sqrt[z]])/(56 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]