Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.4962)

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=-1/2, a₃>=-1/2

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

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

http://functions.wolfram.com/07.27.03.4962.01

Input Form

HypergeometricPFQ[{-(7/2), -(1/2), 1}, {7/2, 4}, -z] == (2 (24 - 1092 z + 5005 z^2))/(9009 z^3) + (1/(9225216 z^3)) (Sqrt[1 + z] (-49152 + 1945677 z - 7392890 z^2 + 4946104 z^3 - 231840 z^4 - 17024 z^5 - 896 z^6)) - (5 (-7 + 84 z - 168 z^2 + 64 z^3) ArcSinh[Sqrt[z]])/(1024 z^(5/2))

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]