Symmetric orthogonal polynomials and the associated orthogonal -polynomials

Author:
A. Sri Ranga

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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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]**T. S. Chihara,*An introduction to orthogonal polynomials*, Gordon and Breach Science Publishers, New York-London-Paris, 1978. Mathematics and its Applications, Vol. 13. MR**0481884****[2]**William B. Jones, Olav NjÈ§stad, 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**, https://doi.org/10.1016/0377-0427(83)90034-1**[3]**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**, https://doi.org/10.1090/S0002-9947-1980-0580900-4**[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.**[5]**A. Sri Ranga,*On a recurrence formula associated with strong distributions*, SIAM J. Math. Anal.**21**(1990), no. 5, 1335–1348. MR**1062408**, https://doi.org/10.1137/0521074**[6]**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**, https://doi.org/10.1017/S0013091500004971**[7]**A. Sri Ranga,*The strong 𝑐-symmetric distribution*, J. Austral. Math. Soc. Ser. A**53**(1992), no. 2, 261–265. MR**1175716****[8]**A. Sri Ranga,*Another quadrature rule of highest algebraic degree of precision*, Numer. Math.**68**(1994), no. 2, 283–294. MR**1283343**, https://doi.org/10.1007/s002110050062**[9]**A. Sri Ranga and E. X. L. de Andrade,*A weight function that appears in the limit and certain associated polynomals*(submitted).**[10]**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).**[11]**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****[12]**A. Sri Ranga and J. H. McCabe,*On pairwise related strong Stieltjes distributions*, Skr. K. Nor. Vidensk. Selsk.**3**(1996), 12. MR**1831078****[13]**G. Szegő,*Orthogonal polynomials*, 4th ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, RI, 1975.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
42C05,
33C45

Retrieve articles in all journals with MSC: 42C05, 33C45

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1291791-7

Keywords:
Orthogonal polynomials,
L-polynomials,
recurrence relations

Article copyright:
© Copyright 1995
American Mathematical Society