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

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=-23/8, b>=a

For fixed z and a=-23/8, b=47/8

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

Input Form

Hypergeometric2F1[-(23/8), 47/8, -(11/2), z] == (1/(4190208 (1 - z)^(17/2))) (Sqrt[1 - z] (4190208 - 20784384 z + 33413536 z^2 - 10530793 z^3 - 9277060 z^4 - 14347606 z^5 - 58710652 z^6 + 270814951 z^7 - 388283544 z^8 + 276164240 z^9 - 100279872 z^10 + 14927616 z^11) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (1047552 - 5523456 z + 9838036 z^2 - 4634097 z^3 - 2258412 z^4 - 2928198 z^5 - 159333944 z^6 + 436120575 z^7 - 514763656 z^8 + 324438224 z^9 - 107743680 z^10 + 14927616 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]