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

Fejzullahu, Bujar

doi:10.1090/S0002-9939-2014-11976-9

Mehler–Heine formulas for orthogonal polynomials with respect to the modified Jacobi weight
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by Bujar Xh. Fejzullahu

Proc. Amer. Math. Soc. 142 (2014), 2035-2045

DOI: https://doi.org/10.1090/S0002-9939-2014-11976-9

Published electronically: February 27, 2014

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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 \[ \omega _{\alpha ,\beta ,h}(x)=h(x) (1-x)^\alpha (1+x)^\beta , \hspace {0.5cm} x\in [-1,1],\] where $\alpha ,\beta >0,$ and with $h$ real analytic and strictly positive on $[-1, 1].$

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