Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.7991)

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=4/3, b>=a

For fixed z and a=4/3, b=14/3

http://functions.wolfram.com/07.23.03.7991.01

Input Form

Hypergeometric2F1[4/3, 14/3, -(11/2), -z] == ((110854656 + 1406398464 z + 8395121664 z^2 + 31712536576 z^3 + 87518379520 z^4 + 204438558720 z^5 + 641803728896 z^6 - 778566502399 z^7 - 15115726086 z^8 - 1655040440 z^9 - 104137376 z^10) Cosh[ArcSinh[Sqrt[z]]/3] - Sqrt[z] Sqrt[1 + z] (36951552 + 442796544 z + 2489614848 z^2 + 8851527168 z^3 + 23119483904 z^4 + 52473422848 z^5 - 372807304189 z^6 + 14327257382 z^7 + 1602971752 z^8 + 104137376 z^9) Sinh[ArcSinh[Sqrt[z]]/3])/ (110854656 (1 + z)^(23/2))

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]