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

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=2, a₂>=2

For fixed z and a₁=2, a₂=5/2, a₃>=5/2

For fixed z and a₁=2, a₂=5/2, a₃=4

For fixed z and a₁=2, a₂=5/2, a₃=4, b₁=-7/2

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

Input Form

HypergeometricPFQ[{2, 5/2, 4}, {-(7/2), 7/2}, -z] == (1/(224 z^2 (1 + z)^8)) (15360 + 120320 z + 410976 z^2 + 799168 z^3 + 969128 z^4 + 762996 z^5 + 484525 z^6 - 23100 z^7 + 4620 z^8) - (15 (1024 + 8704 z + 32640 z^2 + 70720 z^3 + 97240 z^4 + 87516 z^5 + 51051 z^6 + 30030 z^7) ArcSinh[Sqrt[z]])/ (224 Sqrt[1 + z] (z^(5/2) + 8 z^(7/2) + 28 z^(9/2) + 56 z^(11/2) + 70 z^(13/2) + 56 z^(15/2) + 28 z^(17/2) + 8 z^(19/2) + z^(21/2)))

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]