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Some Interpolators Properties of Laguerre Polynomials*

Published online by Cambridge University Press:  20 November 2018

J. Prasad  and
R. B. Saxena
J. Prasad
Affiliation:
University of Alberta, Edmonton
R. B. Saxena
Affiliation:
Lucknow University, Lucknow, India
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In 1955, J. Suranyi and P. Turán [8] introduced the nomenclature (0, 2)-interpolation for the problem of finding polynomials of degree ≤ 2n-1 whose values and second derivatives are prescribed in certain given nodes. In a series of papers ([2], [3], [8]) Professor Turán and his associates discussed the problems of existence, uniqueness, explicit representation and convergence of such interpolatory 2 polynomials when the nodes are the zeros of (1-x2) P′n- 1(x), Pn- 1(x) being the Legendre polynomial of degree n - 1.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 4 , October 1967 , pp. 559 - 571
Copyright
Copyright © Canadian Mathematical Society 1967

Footnotes

**

The second author acknowledges financial support from the Canadian Mathematical Congress during the Summer of 1966.

*

We express our gratitude to Prof. A. Sharma for his generous help in preparation of this paper.

References

1. J., Balázs Sûlyozott, (0, 2 ) - interpolâciô ultraszfèrik us polinomok győkein. A. Magyar Tud. akad. Kozlemenyei vol XI (3) 1966 pp. 305-338.Google Scholar
2. Balázs, J., and Turan, P. Noteson interpolation II, Acta Math. Acad. Sci. Hung., 8 (1955) pp. 201-215.Google Scholar
3. J., Balázs and P., Turán Notes on interpolation III, ibid, 9 (1955) pp. 195-214.Google Scholar
4. Kis, O., On trigonometric interpolation (Russian) ibid 11 (1966) pp. 255-276.Google Scholar
5. K. K, Mathur and A., Sharma Some interpolatory properties of Hermite polynomials, ibid (12) (1966) pp. 192-207.Google Scholar
6. Sansone, G. Orthogonal functions, Inter. Oule, Inc. New York vol. 9 (1955)Google Scholar
7. Sharma, A. and A. K., Varma Trigonometric interpolation, Duke Math. Journal 32 (1966) pp. 341-357.Google Scholar
8. Suranyi, J. and P., Turán, Notes on interpolation I. Acta Math. Acad. Hung. 6 (1955) pp. 67-79.Google Scholar
9. Szego, G. Orthogonal Polynomials, Amer. Math. Soc. Collo. Pub. vol. 23 (1955). University of Alberta, Edmonton Lucknow University, Lucknow, India Google Scholar