Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8260)

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=7/3, b>=a

For fixed z and a=7/3, b=8/3

http://functions.wolfram.com/07.23.03.8260.01

Input Form

Hypergeometric2F1[7/3, 8/3, -(9/2), z] == (1/(839808 (-1 + z)^9)) ((1/Sqrt[1 - z]) (9 (-93312 + 1020672 z - 5273216 z^2 + 17648128 z^3 - 47134976 z^4 + 168303104 z^5 + 264556529 z^6 + 31617428 z^7) Cos[ArcSin[Sqrt[z]]/3]) - Sqrt[z] (279936 - 2865024 z + 13825024 z^2 - 43425280 z^3 + 111807744 z^4 + 1009576043 z^5 + 202734628 z^6) Sin[ArcSin[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]