[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2003.40.4.699

THE DUAL OF A FORMULA OF VISKOV

Szafraniec, Franciszek Hugon (Instytut Matematyki, Uniwersytet Jagiellonski)

Publication Information

Bulletin of the Korean Mathematical Society / v.40, no.4, 2003 , pp. 699-701 More about this Journal

Abstract

This minipaper offers a formula which is dual to that of Viskov [5]. While Viskov's can be thought of as a rising formula for Laguerre polynomials, ours is precisely the lowering one. Besides documenting the formula, which seems to be missing, we want to provide a (rather elementary) operator theory argument instead of making crude calculations. In other words, the annihilation and creation operators are confronted with lowering and rising formulae; they are often failed to be distinguished.

Keywords

Laguerre polynomials; raising and lowering formulae; weighted shift operator;

Citations & Related Records

Reference

1	L. B. Redei identity for Laguerre polynomials / [ O.V.Viskov ] / Acta. Sci. Math.
2	An identity for Laguerre polynomials / [ L.B.Redei ] / Acta Sci. Math.
3	The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue / [ R.Koekoek;R.F.Swarttouw ] / Delft University of Technology, Report of the Department of Technical Mathematics and Informatics no. 98-17
4	A few assorted questions about unbounded subnormal operators / [ Jan Stochel;F.H.Szafraniec ] / Univ. Iagel. Acta Math.
5	Orthogonal polynomials and subnormality of related shift operators, "Orthogonal polynomials and their applications" / [ F.H.Szafraniec ] / Proc. Segovia (Spain), 1986 Monogr. Acad. Cienc. Zaragoza R.-C. Plalacios