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Unformatted text preview: series about x is equivalent to the boundedness of the functions in a deleted neighborhood of x , i.e., a subset of the xyplane of the form { ( x,y ) ∈ R 2  < p ( xx ) 2 + y 2 < δ } for some δ > 0. In the case P ( x ), Q ( x ), and R ( x ) are polynomials, this is equivalent to requiring that the limits lim x → x ( xx ) p ( x ) = ( xx ) Q ( x ) P ( x ) , (4a) lim x → x ( xx ) 2 q ( x ) = ( xx ) 2 R ( x ) P ( x ) (4b) exist and are ﬁnite. Date : February 8, 2011. 1...
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 Winter '11
 Kwa
 Differential Equations, Equations, lim, regular singular points, KIAM HEONG KWA, convergent Taylor

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