Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1379)

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=1/2

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

http://functions.wolfram.com/07.27.03.1379.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 1/2}, {-(1/2), 5/2}, -z] == (3 Sqrt[1 + z] (-245 + 21345 z + 124102 z^2 - 222216 z^3 + 35632 z^4))/ (81920 z) - (21 (-7 - 175 z + 5600 z^3 - 4480 z^4 + 384 z^5) ArcSinh[Sqrt[z]])/(16384 z^(3/2))

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]