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On the connection coefficients of the Chebyshev-Boubaker polynomials
1School of Science, Waterford Institute of Technology, Waterford, Ireland. pbarry@wit.ie
Thescientificworldjournal
|August 31, 2013
Summary
Chebyshev-Boubaker polynomials, defined by Riordan arrays, have their connection coefficients studied. Riordan array techniques provide closed-form expressions and recurrence relations for these coefficients.
Area of Science:
- Mathematics
- Orthogonal Polynomials
- Combinatorics
Background:
- Orthogonal polynomials are fundamental in various mathematical fields.
- Chebyshev-Boubaker polynomials form a class of orthogonal polynomials.
- Riordan arrays offer a combinatorial framework for sequence analysis.
Purpose of the Study:
- To investigate the connection coefficients of Chebyshev-Boubaker polynomials.
- To demonstrate the application of Riordan array techniques in this context.
- To derive closed-form expressions and recurrence relations for these coefficients.
Main Methods:
- Utilizing the properties of Riordan arrays.
- Applying combinatorial methods to analyze coefficient arrays.
- Deriving explicit formulas for connection coefficients.
Main Results:
- Established a connection between Riordan arrays and Chebyshev-Boubaker polynomials.
- Derived closed-form expressions for the connection coefficients.
- Obtained recurrence relations defining these coefficients.
Conclusions:
- Riordan array techniques are effective for studying Chebyshev-Boubaker polynomials.
- The derived expressions and relations offer new insights into these polynomials.
- This work bridges combinatorics and the theory of orthogonal polynomials.
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