Symmetric orthogonal polynomials and the associated orthogonal $L$-polynomials
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- by A. Sri Ranga PDF
- Proc. Amer. Math. Soc. 123 (1995), 3135-3141 Request permission
Abstract:
We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained. Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function $(1 + k{x^2}) {(1 - {x^2})^{ - 1/2}},k > 0$.References
- T. S. Chihara, An introduction to orthogonal polynomials, Mathematics and its Applications, Vol. 13, Gordon and Breach Science Publishers, New York-London-Paris, 1978. MR 0481884
- William B. Jones, Olav Njȧstad, and W. J. Thron, Two-point Padé expansions for a family of analytic functions, J. Comput. Appl. Math. 9 (1983), no. 2, 105–123. MR 709210, DOI 10.1016/0377-0427(83)90034-1
- William B. Jones, W. J. Thron, and Haakon Waadeland, A strong Stieltjes moment problem, Trans. Amer. Math. Soc. 261 (1980), no. 2, 503–528. MR 580900, DOI 10.1090/S0002-9947-1980-0580900-4 O. Njåstad and W. J. Thron, The theory of sequences of L-polynomials, Padé Approximants and Continued Fractions (H. Waadeland and H. Wallin, eds.), Det Kongelige Norsk Videnskabers Selskab, vol. 1, Universitetsforlaget, Trondeihm, 1983, pp. 54-91.
- A. Sri Ranga, On a recurrence formula associated with strong distributions, SIAM J. Math. Anal. 21 (1990), no. 5, 1335–1348. MR 1062408, DOI 10.1137/0521074
- A. Sri Ranga and J. H. McCabe, On the extensions of some classical distributions, Proc. Edinburgh Math. Soc. (2) 34 (1991), no. 1, 19–29. MR 1093173, DOI 10.1017/S0013091500004971
- A. Sri Ranga, The strong $c$-symmetric distribution, J. Austral. Math. Soc. Ser. A 53 (1992), no. 2, 261–265. MR 1175716, DOI 10.1017/S1446788700035837
- A. Sri Ranga, Another quadrature rule of highest algebraic degree of precision, Numer. Math. 68 (1994), no. 2, 283–294. MR 1283343, DOI 10.1007/s002110050062 A. Sri Ranga and E. X. L. de Andrade, A weight function that appears in the limit and certain associated polynomals (submitted). A. Sri Ranga, E. X. L. de Andrade, and J. H. McCabe, Some consequences of symmetry in strong distributions, J. Math. Anal. Appl. (to appear).
- A. Sri Ranga and C. F. Bracciali, A continued fraction associated with a special Stieltjes function, Comm. Anal. Theory Contin. Fractions 3 (1994), 60–64. MR 1293985
- A. Sri Ranga and J. H. McCabe, On pairwise related strong Stieltjes distributions, Skr. K. Nor. Vidensk. Selsk. 3 (1996), 12. MR 1831078 G. Szegő, Orthogonal polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, RI, 1975.
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3135-3141
- MSC: Primary 42C05; Secondary 33C45
- DOI: https://doi.org/10.1090/S0002-9939-1995-1291791-7
- MathSciNet review: 1291791