Abstract
AbstractThe principal aim of the current article is to establish new formulas of Chebyshev polynomials of the sixth-kind. Two different approaches are followed to derive new connection formulas between these polynomials and some other orthogonal polynomials. The connection coefficients are expressed in terms of terminating hypergeometric functions of certain arguments; however, they can be reduced in some cases. New moment formulas of the sixth-kind Chebyshev polynomials are also established, and in virtue of such formulas, linearization formulas of these polynomials are developed.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference27 articles.
1. Gil, A., Segura, J., Temme, N.M.: Numerical Methods for Special Functions. SIAM, Philadelphia (2007)
2. Mason, J.C., Handscomb, D.C.: Chebyshev Polynomials. Chapman & Hall/ CRC, Boca Raton (2003)
3. Ralston, A.: Numerical integration methods for the solution of ordinary differential equations. In: Ralston, A., Wilf, H.S. (eds.) Mathematical Methods for Digital Computers, vol. 1 (1960)
4. Gautschi, W.: On mean convergence of extended Lagrange interpolation. J. Comput. Appl. Math. 43(1–2), 19–35 (1992)
5. Masjed-Jamei, M.: Some new classes of orthogonal polynomials and special functions: a symmetric generalization of Sturm–Liouville problems and its consequences. Ph.D. thesis, Department of Mathematics, University of Kassel, Kassel, Germany (2006)
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