Identity-Type Functions and Polynomials. (30th April 2007)

• Record Type: Journal Article
• Authors: Chaudhry, M. Aslam; Qadir, Asghar
• Other Names: Begehr Heinrich Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Voume 2007(2007)
• Publication Date: 2007-04-30
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2007/94204
• Languages: English
• ISSNs: 0161-1712

Abstract

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.