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On Bessel Polynomials

Published online by Cambridge University Press:  20 November 2018

R. P. Agarwal*
Affiliation:
Bedford College, London
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Recently a number of papers have been written on Bessel polynomials which arise as the solutions of the classical wave equation in spherical coordinates. Krall and Frink (5) studied in some detail the properties of these polynomials yn(x, a, b) defined as

(1) .

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Brafman, Fred, A set of generating functions for Bessel polynomials, Proc. Amer. Math. Soc. 4 (1953), 275–277.Google Scholar
2. Burchnall, J. L., The Bessel polynomials, Can. J. Math., 8 (1951), 62–68.Google Scholar
3. Burchnall, J. L. and Chaundy, T. W., Commutative Ordinary Differential Operators; II. The identity Pn = Qm , Proc. Roy. Soc. A 134 (1931), 471–485.Google Scholar
4. Burchnall, J. L. and Chaundy, T. W., Expansions of Appell's double hyper geometric functions, Quart. J. Math. (Oxford), 11 (1940), 249–70.Google Scholar
5. Krall, H. L. and Frink, O., A new class of orthogonal polynomials: The Bessel polynomials, Trans. Amer. Math. Soc, 65 (1949), 100–115.Google Scholar
6. Rainville, E. D., Generating functions for Bessel and related polynomials, Can. J. Math., 5 (1953), 104–106.Google Scholar
7. Szegö, G., Orthogonal Polynomials (Amer. Math. Soc. Colloquium Publications, Vol. 23, 1939).Google Scholar
8. Whittaker, E. T. and Watson, G. N., Modern Analysis (Cambridge, 1920).Google Scholar