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

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=-7/8, b>=a

For fixed z and a=-7/8, b=45/8

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

Input Form

Hypergeometric2F1[-(7/8), 45/8, -(23/4), z] == ((1 + Sqrt[1 - z])^(3/4) (2 (82526576 - 739151072 z + 2866889685 z^2 - 6157282813 z^3 + 7499943808 z^4 - 3759450786 z^5 + 9569399021 z^6 - 8092624865 z^7 + 3787591470 z^8 - 974973312 z^9 + 108421632 z^10) + (1/Sqrt[1 - z]) (165053152 - 1560828720 z + 6452298798 z^2 - 15006983365 z^3 + 20526394503 z^4 - 13784652882 z^5 - 31252583908 z^6 + 43656795351 z^7 - 30125853537 z^8 + 12311353888 z^9 - 2846889216 z^10 + 289124352 z^11)))/(330106304 2^(3/4) (-1 + z)^10)

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]