Symmetric orthogonal polynomials and the associated orthogonal polynomials
Author:
A. Sri Ranga
Journal:
Proc. Amer. Math. Soc. 123 (1995), 31353141
MSC:
Primary 42C05; Secondary 33C45
MathSciNet review:
1291791
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal Lpolynomials. 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, 1978. Mathematics and its
Applications, Vol. 13. MR 0481884
(58 #1979)
 [2]
William
B. Jones, Olav
Njȧstad, and W.
J. Thron, Twopoint Padé expansions for a family of analytic
functions, J. Comput. Appl. Math. 9 (1983),
no. 2, 105–123. MR 709210
(84j:30057), http://dx.doi.org/10.1016/03770427(83)900341
 [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 (81j:30055), http://dx.doi.org/10.1090/S00029947198005809004
 [4]
O. Njåstad and W. J. Thron, The theory of sequences of Lpolynomials, Padé Approximants and Continued Fractions (H. Waadeland and H. Wallin, eds.), Det Kongelige Norsk Videnskabers Selskab, vol. 1, Universitetsforlaget, Trondeihm, 1983, pp. 5491.
 [5]
A.
Sri Ranga, On a recurrence formula associated with strong
distributions, SIAM J. Math. Anal. 21 (1990),
no. 5, 1335–1348. MR 1062408
(91c:30068), http://dx.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 (92b:30003), http://dx.doi.org/10.1017/S0013091500004971
 [7]
A.
Sri Ranga, The strong 𝑐symmetric distribution, J.
Austral. Math. Soc. Ser. A 53 (1992), no. 2,
261–265. MR 1175716
(93f:42046)
 [8]
A.
Sri Ranga, Another quadrature rule of highest algebraic degree of
precision, Numer. Math. 68 (1994), no. 2,
283–294. MR 1283343
(95c:65047), http://dx.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.
 [1]
 T. S. Chihara, An introduction to orthogonal polynomials, Math. Appl., Gordon and Breach, New York, 1978. MR 0481884 (58:1979)
 [2]
 W. B. Jones, O. Njåstad, and W. J. Thron, Twopoint Padé expansions for a family of analytic functions, J. Comput. Appl. Math. 9 (1983), 105123. MR 709210 (84j:30057)
 [3]
 W. B. Jones, W. J. Thron, and H. Waadeland, A strong Stieltjes moment problem, Trans. Amer. Math. Soc. 261 (1980), 503528. MR 580900 (81j:30055)
 [4]
 O. Njåstad and W. J. Thron, The theory of sequences of Lpolynomials, Padé Approximants and Continued Fractions (H. Waadeland and H. Wallin, eds.), Det Kongelige Norsk Videnskabers Selskab, vol. 1, Universitetsforlaget, Trondeihm, 1983, pp. 5491.
 [5]
 A. Sri Ranga, On a recurrence formula associated with strong distributions, SIAM J. Math. Anal. 21 (1990), 13351348. MR 1062408 (91c:30068)
 [6]
 A. Sri Ranga and J. H. McCabe, On the extensions of some classical distributions, Proc. Edinburgh Math. Soc. 34 (1991), 6167. MR 1093173 (92b:30003)
 [7]
 A. Sri Ranga, The strong csymmetric distribution, J. Austral. Math. Soc. Ser. A 53 (1992), 6165. MR 1175716 (93f:42046)
 [8]
 , Another quadrature rule of highest algebraic degree of precision, Numer. Math. 68 (1994), 283294. MR 1283343 (95c:65047)
 [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 Continued Fractions 3 (1994), 6064. MR 1293985
 [12]
 A. Sri Ranga and J. H. McCabe, On pairwise related strong Stieltjes distributions (submitted). MR 1831078
 [13]
 G. Szegő, Orthogonal polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, RI, 1975.
Similar Articles
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:
http://dx.doi.org/10.1090/S00029939199512917917
PII:
S 00029939(1995)12917917
Keywords:
Orthogonal polynomials,
Lpolynomials,
recurrence relations
Article copyright:
© Copyright 1995 American Mathematical Society
