Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.at36)

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=2, a₂>=2

For fixed z and a₁=2, a₂=2, a₃>=2

For fixed z and a₁=2, a₂=2, a₃=7/2

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

http://functions.wolfram.com/07.27.03.at36.01

Input Form

HypergeometricPFQ[{2, 2, 7/2}, {-(7/2), -(5/2)}, z] == (1/(100 (-1 + z)^13)) (-100 + 1140 z - 6584 z^2 - 6440 z^3 + 5837364 z^4 + 282576668 z^5 + 1917906672 z^6 + 3611730672 z^7 + 2160563460 z^8 + 375931668 z^9 + 11513916 z^10 - 65811 z^11) - (693 (-11264 z^(9/2) - 194048 z^(11/2) - 770688 z^(13/2) - 974400 z^(15/2) - 412440 z^(17/2) - 50652 z^(19/2) - 939 z^(21/2) + 6 z^(23/2)) ArcSin[Sqrt[z]])/(20 Sqrt[1 - z] (-1 + 13 z - 78 z^2 + 286 z^3 - 715 z^4 + 1287 z^5 - 1716 z^6 + 1716 z^7 - 1287 z^8 + 715 z^9 - 286 z^10 + 78 z^11 - 13 z^12 + z^13))

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]