Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.7588)

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=1/3, b>=a

For fixed z and a=1/3, b=17/3

http://functions.wolfram.com/07.23.03.7588.01

Input Form

Hypergeometric2F1[1/3, 17/3, -(9/2), -z] == ((47029248 + 516160512 z + 2605612032 z^2 + 8087806976 z^3 + 17816494080 z^4 + 36646500352 z^5 + 7019101797 z^6 + 3160270012 z^7 + 1024954888 z^8 + 205009120 z^9 + 18868096 z^10) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[z] Sqrt[1 + z] (-15676416 - 161021952 z - 756429824 z^2 - 2175416320 z^3 - 4460431360 z^4 + 5764418769 z^5 + 2718774708 z^6 + 929525864 z^7 + 195575072 z^8 + 18868096 z^9) Sinh[ArcSinh[Sqrt[z]]/3])/ (47029248 (1 + z)^(21/2))

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]