Title of article
Some Orthogonal Polynomials Related to Elliptic Functions Original Research Article
Author/Authors
Mourad E.H. Ismail ، نويسنده , , Christina T?nnesen-Friedman and Galliano Valent، نويسنده , , Gang J. Yoon، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2001
Pages
28
From page
251
To page
278
Abstract
We characterize the orthogonal polynomials in a class of polynomials defined through their generating functions. This led to three new systems of orthogonal polynomials whose generating functions and orthogonality relations involve elliptic functions. The Hamburger moment problems associated with these polynomials are indeterminate. We give infinite families of weight functions in each case. The different polynomials treated in this work are also polynomials in a parameter and as functions of this parameter they are orthogonal with respect to unique measures, which we find explicitly. Through a quadratic transformation we find a new exactly solvable birth and death process with quartic birth and death rates.
Journal title
Journal of Approximation Theory
Serial Year
2001
Journal title
Journal of Approximation Theory
Record number
851958
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