Identity-Type Functions and Polynomials
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/94204 |
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| _version_ | 1850223330599108608 |
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| author | M. Aslam Chaudhry Asghar Qadir |
| author_facet | M. Aslam Chaudhry Asghar Qadir |
| author_sort | M. Aslam Chaudhry |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5e03bda1ef1647d08bd2c7a6bf809e6c |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5e03bda1ef1647d08bd2c7a6bf809e6c2025-08-20T02:06:00ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/9420494204Identity-Type Functions and PolynomialsM. Aslam Chaudhry0Asghar Qadir1Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaDepartment of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaFor 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.http://dx.doi.org/10.1155/2007/94204 |
| spellingShingle | M. Aslam Chaudhry Asghar Qadir Identity-Type Functions and Polynomials International Journal of Mathematics and Mathematical Sciences |
| title | Identity-Type Functions and Polynomials |
| title_full | Identity-Type Functions and Polynomials |
| title_fullStr | Identity-Type Functions and Polynomials |
| title_full_unstemmed | Identity-Type Functions and Polynomials |
| title_short | Identity-Type Functions and Polynomials |
| title_sort | identity type functions and polynomials |
| url | http://dx.doi.org/10.1155/2007/94204 |
| work_keys_str_mv | AT maslamchaudhry identitytypefunctionsandpolynomials AT asgharqadir identitytypefunctionsandpolynomials |