Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5qn)

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=-47/8, b>=a

For fixed z and a=-47/8, b=45/8

http://functions.wolfram.com/07.23.03.b5qn.01

Input Form

Hypergeometric2F1[-(47/8), 45/8, -(23/4), z] == ((1 + Sqrt[1 - z])^(3/4) (-165053152 - 154288816 z - 170081230 z^2 - 225236649 z^3 - 390541956 z^4 - 1035252933 z^5 + 171358229328 z^6 - 576579843840 z^7 + 753375068160 z^8 - 446372315136 z^9 + 100590944256 z^10 + (1/Sqrt[1 - z]) (2 (-82526576 - 35881120 z - 36152589 z^2 - 55297055 z^3 - 120286519 z^4 - 395328609 z^5 - 91477267596 z^6 + 430290967392 z^7 - 804633882624 z^8 + 754193104896 z^9 - 354862497792 z^10 + 67060629504 z^11))))/ (330106304 2^(3/4) (-1 + z)^5)

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]