Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5123)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-14/3, b>=a

For fixed z and a=-14/3, b=-13/3

http://functions.wolfram.com/07.23.03.5123.01

Input Form

Hypergeometric2F1[-(14/3), -(13/3), 11/2, z] == (6561 (-3 Sqrt[z] (49545216 - 1163657216 z + 15062007808 z^2 - 164609392640 z^3 - 18302094409577 z^4 - 38569904625503 z^5 + 12854838466288 z^6 + 34813837018168 z^7 + 8972380191520 z^8 + 381604855936 z^9) Cos[ArcSin[Sqrt[z]]/3] + Sqrt[1 - z] (445906944 - 10340794368 z + 132552851456 z^2 - 1443536568320 z^3 + 25912505794560 z^4 + 277879136845673 z^5 + 524384058335344 z^6 + 290815983194808 z^7 + 46537374809696 z^8 + 1441278800512 z^9) Sin[ArcSin[Sqrt[z]]/3]))/ (417809724066539035 Sqrt[1 - z] z^(9/2))

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,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},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]