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Mehler-Heine formulas for orthogonal polynomials with respect to the modified Jacobi weight


Author: Bujar Xh. Fejzullahu
Journal: Proc. Amer. Math. Soc. 142 (2014), 2035-2045
MSC (2010): Primary 42C05; Secondary 42C10
DOI: https://doi.org/10.1090/S0002-9939-2014-11976-9
Published electronically: February 27, 2014
MathSciNet review: 3182023
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Abstract: In this paper the ladder operator approach has been applied to deduce the Mehler-Heine type formulas for orthogonal polynomials with respect to the modified Jacobi weight

$\displaystyle \omega _{\alpha ,\beta ,h}(x)=h(x) (1-x)^\alpha (1+x)^\beta , \hspace {0.5cm} x\in [-1,1],$

where $ \alpha ,\beta >0,$ and with $ h$ real analytic and strictly positive on $ [-1, 1].$

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Additional Information

Bujar Xh. Fejzullahu
Affiliation: Faculty of Mathematics and Sciences, University of Prishtina, Mother Teresa 5, 10000 Prishtinë, Kosovë
Email: bujarfe@yahoo.com

DOI: https://doi.org/10.1090/S0002-9939-2014-11976-9
Keywords: Orthogonal polynomials, ladder operator, Mehler-Heine formulas
Received by editor(s): February 5, 2012
Received by editor(s) in revised form: June 28, 2012
Published electronically: February 27, 2014
Communicated by: Walter Van Assche
Article copyright: © Copyright 2014 American Mathematical Society

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