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Sums of powers of the zeros of the Bessel polynomials

Published online by Cambridge University Press:  26 February 2010

F. T. Howard
F. T. Howard
Affiliation:
Department of Mathematics and Computer Science, Wake Forest University, Box 7311, Reynolda Station, Winston-Salem, North Carolina, 27109, U.S.A.
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Abstract

Let be the sum of the m-th powers of the zeros of the Bessel polynomial yn(x). It is known that for m = 0, 1, 2, …,

where cm(v) is the Hawkins polynomial. In this paper we find rational functions wm(v) such that for m = 0, 1, 2, …

Type
Research Article
Information
Mathematika , Volume 37 , Issue 2 , December 1990 , pp. 305 - 315
Copyright
Copyright © University College London 1990

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References

1. Burchnall, J.. The Bessel polynomials. Canad. J. Math., 3 (1951), 62–68.CrossRefGoogle Scholar
2. Comtet, L.. Advanced Combinatorics (Reidel, Dordrecht/Boston, 1974).CrossRefGoogle Scholar
3. Grosswald, E.. Bessel Polynomials, Lecture Notes in Mathematics, 698 (Springer, Berlin, 1978).CrossRefGoogle Scholar
4. Hawkins, J.. On a Zeta Function Associated with Bessel's Equation, Doctoral Thesis (University of Illinois, 1983).Google Scholar
5. Kishore, N.. The Rayleigh function. Proc. Amer. Math. Soc., 14 (1963), 527–533.CrossRefGoogle Scholar
6. Kishore, N.. The Rayleigh polynomial. Proc. Amer. Math. Soc., 15 (1964), 911–917.CrossRefGoogle Scholar
7. Kishore, N.. A structure of the Rayleigh polynomial. Duke Math. J., 31 (1964), 513–518.CrossRefGoogle Scholar
8. Stolarsky, K. B.. Singularities of Bessel-zeta functions and Hawkins' polynomials. Mathematika, 32 (1985), 96–103.CrossRefGoogle Scholar
9. Watson, G. N.. A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge, 1966).Google Scholar