Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5428)

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=14/3

http://functions.wolfram.com/07.23.03.5428.01

Input Form

Hypergeometric2F1[-(14/3), 14/3, 11/2, -z] == (1/(4690180495 z^(9/2))) (6561 (Sqrt[z/(1 + z)] (-2268 + 192 z - 1236 z^2 + 5544 z^3 + 654027 z^4 + 2656875 z^5 + 4521608 z^6 + 3948048 z^7 + 1754688 z^8 + 316160 z^9) Cosh[ArcSinh[Sqrt[z]]/3] + (6804 - 2592 z + 5372 z^2 - 19096 z^3 + 189420 z^4 + 1414699 z^5 + 3106792 z^6 + 3189264 z^7 + 1596608 z^8 + 316160 z^9) Sinh[ArcSinh[Sqrt[z]]/3]))

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]