Loureiro, Ana F. and Maroni, P. and Rocha, Z. da (2006) The generalised Bochner condition about classical orthogonal polynomials revisited. Journal of Mathematical Analysis and Applications, 322 (2). pp. 645-667. ISSN 0022-247X.
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We bring a new proof for showing that an orthogonal polynomial sequence is classical if and only if any of its polynomial fulfils a certain differential equation of order 2k, for some k⩾1. So, we build those differential equations explicitly. If k=1, we get the Bochner's characterization of classical polynomials. With help of the formal computations made in Mathematica, we explicitly give those differential equations for k=1,2 and 3 for each family of the classical polynomials. Higher order differential equations can be obtained similarly.
|Uncontrolled keywords:||Classical orthogonal polynomials; Classical forms; Bochner's differential equation|
|Subjects:||Q Science > QA Mathematics (inc Computing science) > QA351 Special functions|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics|
|Depositing User:||Ana F. Loureiro|
|Date Deposited:||11 Oct 2012 15:21|
|Last Modified:||20 Feb 2013 14:41|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/31538 (The current URI for this page, for reference purposes)|
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