Identity-Type Functions and Polynomials

M. Aslam Chaudhry and Asghar Qadir

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-10

Abstract:

For a noncommuting product of functions, similar to convolutions, an “identity-type function” leaving a specific function invariant is defined. It is evaluated for any choice of function on which it acts by solving a functional equation. A closed-form representation for the identity-type function of ( 1 + t ) − b ( b > 0 ) is obtained, which is a solution of a second-order linear differential equation with given boundary conditions. It yields orthogonal polynomials whose graphs are also given. The relevance for solution of boundary value problems by a series and convergence of the series are briefly discussed.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:094204

DOI: 10.1155/2007/94204

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