Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.caed)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a>0

For fixed z and a=27/8, b>=a

For fixed z and a=27/8, b=37/8

http://functions.wolfram.com/07.23.03.caed.01

Input Form

Hypergeometric2F1[27/8, 37/8, -(11/2), z] == -((1/(1306624 (1 - z)^(27/2))) (Sqrt[1 - z] (-1306624 + 21061888 z - 165979296 z^2 + 872608173 z^3 - 3621025608 z^4 + 14401618863 z^5 - 97216874522 z^6 - 280357686901 z^7 - 118308196692 z^8 - 7668422663 z^9 + 52344182 z^10) Cos[(3 ArcSin[Sqrt[z]])/4] + 2 Sqrt[z] (-489984 + 7969664 z - 63349398 z^2 + 335617029 z^3 - 1400421397 z^4 + 5572479717 z^5 - 89507654121 z^6 - 175079665033 z^7 - 64037933991 z^8 - 3847297377 z^9 + 26172091 z^10) Sin[(3 ArcSin[Sqrt[z]])/4]))

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]