Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5120)

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/07.23.03.5120.01

Input Form

Hypergeometric2F1[-(14/3), -(13/3), 7/2, -z] == (81 (9 Sqrt[z] (-262144 - 8650752 z + 2677195821 z^2 - 10585971947 z^3 + 1709376096 z^4 + 10627948632 z^5 - 4119490720 z^6 + 233493120 z^7) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (7077888 + 231473152 z + 8325169152 z^2 - 146893458567 z^3 + 413676503840 z^4 - 319986586632 z^5 + 68028439200 z^6 - 2696508800 z^7) Sinh[ArcSinh[Sqrt[z]]/3]))/(2178281940005 z^(5/2) Sqrt[1 + z])

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]