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

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=41/8, b>=a

For fixed z and a=41/8, b=47/8

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

Input Form

Hypergeometric2F1[41/8, 47/8, -(11/2), z] == (1/(12570624 (1 - z)^(33/2))) (Sqrt[1 - z] (12570624 - 270339840 z + 2939836640 z^2 - 22258815579 z^3 + 140654727928 z^4 - 918678837076 z^5 + 11323151079240 z^6 + 63233548666430 z^7 + 68567239117640 z^8 + 21133710398700 z^9 + 1595477886744 z^10 + 9730570245 z^11) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (3142656 - 68567040 z + 755662076 z^2 - 5785645723 z^3 + 36810107048 z^4 - 239972777044 z^5 + 104207900650000 z^6 + 289754145894910 z^7 + 214959260173880 z^8 + 48813352933740 z^9 + 2724895302036 z^10 + 9730570245 z^11) Sin[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]