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Identity-Type Functions and Polynomials

Author

Listed:
  • M. Aslam Chaudhry
  • Asghar Qadir

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.

Suggested Citation

  • M. Aslam Chaudhry & Asghar Qadir, 2007. "Identity-Type Functions and Polynomials," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-10, April.
    • Handle: RePEc:hin:jijmms:094204
    DOI: 10.1155/2007/94204
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