Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1490)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃>=-7/2

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

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

http://functions.wolfram.com/07.27.03.1490.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 1}, {1/2, 4}, -z] == -((2 (120 + 2028 z + 20449 z^2))/(552123 z^3)) + (1/(8833968 z^3)) (Sqrt[1 + z] (3840 + 62976 z + 623360 z^2 + 8529920 z^3 - 38974575 z^4 + 23737640 z^5 - 2069764 z^6)) + (35 (-429 Sqrt[z] + 858 z^(3/2) - 312 z^(5/2) + 16 z^(7/2)) ArcSinh[Sqrt[z]])/6864

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]