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Estimation of a Stieltjes function expanded to Taylor series at complex conjugate points

✍ Scribed by Stanisław Tokarzewski; Alphonse Ph. Magnus; Jacek Gilewicz


Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
623 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis


Taylor series expansions of a Stieltjes function f in various complex conjugate points are used to construct the so called unified continued fractions (UCF) terminated on P-th step by a remainder f U P named tail of f. We prove that, if f is a Stieltjes function then its tail f U P is also a Stieltjes function. The estimations of f are obtained in what follows. Numerical calculations of the new complex bounds on f generated by complex conjugate input data are carried out.