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

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=3, a₂>=3

For fixed z and a₁=3, a₂=3, a₃>=3

For fixed z and a₁=3, a₂=3, a₃=7/2

For fixed z and a₁=3, a₂=3, a₃=7/2, b₁=-7/2

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

Input Form

HypergeometricPFQ[{3, 3, 7/2}, {-(7/2), 3/2}, z] == (1/(11200 (-1 + z)^11)) (-11200 + 190400 z - 1742272 z^2 + 13180992 z^3 - 161103360 z^4 - 743991960 z^5 - 548658860 z^6 - 84109613 z^7 - 1455302 z^8) - (1287 z^(9/2) (8008 + 17108 z + 7983 z^2 + 808 z^3 + 8 z^4) ArcSin[Sqrt[z]])/(320 Sqrt[1 - z] (-1 + 11 z - 55 z^2 + 165 z^3 - 330 z^4 + 462 z^5 - 462 z^6 + 330 z^7 - 165 z^8 + 55 z^9 - 11 z^10 + z^11))

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]