Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5143)

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=-10/3

http://functions.wolfram.com/07.23.03.5143.01

Input Form

Hypergeometric2F1[-(14/3), -(10/3), 7/2, z] == -((81 (Sqrt[z] (1179648 - 33292288 z - 7535514153 z^2 - 20561837955 z^3 + 6788135828 z^4 + 18166878840 z^5 + 3167193120 z^6 + 7256960 z^7) Cos[ArcSin[Sqrt[z]]/3] + Sqrt[1 - z] (-3538944 + 98828288 z - 2945187840 z^2 - 41496583011 z^3 - 87218836252 z^4 - 44569278600 z^5 - 4625842080 z^6 + 7256960 z^7) Sin[ArcSin[Sqrt[z]]/3]))/ (690674761465 Sqrt[1 - z] z^(5/2)))

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]