Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8553)

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=10/3, b>=a

For fixed z and a=10/3, b=11/3

http://functions.wolfram.com/07.23.03.8553.01

Input Form

Hypergeometric2F1[10/3, 11/3, -(11/2), -z] == ((80621568 + 1191407616 z + 8501207040 z^2 + 39797137408 z^3 + 143592198144 z^4 + 478528622592 z^5 + 2533198413824 z^6 - 7372412514255 z^7 + 2778731105892 z^8 - 154970628944 z^9) Cosh[ArcSinh[Sqrt[z]]/3] + 9 Sqrt[z] Sqrt[1 + z] (-2985984 - 42024960 z - 285515776 z^2 - 1276166144 z^3 - 4440616960 z^4 - 14686683136 z^5 + 273569326405 z^6 - 163978315204 z^7 + 13101399984 z^8) Sinh[ArcSinh[Sqrt[z]]/3])/(80621568 (1 + z)^(25/2))

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]