Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3001)

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=-5/2, a₃>=-5/2

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

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

http://functions.wolfram.com/07.27.03.3001.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 2}, {5/2, 4}, -z] == (8 (4 + 143 z))/(99099 z^3) + (1/(405909504 z^3)) (Sqrt[1 + z] (-131072 - 4620288 z - 8111635 z^2 + 327887050 z^3 - 433814328 z^4 + 92300432 z^5 - 798336 z^6)) - (5 (-231 - 1848 z + 9504 z^2 - 7040 z^3 + 896 z^4) ArcSinh[Sqrt[z]])/ (45056 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]