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Sums of powers of the zeros of the Bessel polynomials
Author(s) -
Howard F. T.
Publication year - 1990
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300013012
Subject(s) - mathematics , bessel function , polynomial , bessel polynomials , rational function , pure mathematics , combinatorics , discrete mathematics , orthogonal polynomials , mathematical analysis , difference polynomials , wilson polynomials
Letσ m ( n )be the sum of the m ‐th powers of the zeros of the Bessel polynomial y n ( x ). It is known that for m = 0, 1, 2, …,σ − ( m + 1 )( n )=( − 1 )m + 1c m ( ( 2 n + 1 ) / 2 ) ,where c m ( v ) is the Hawkins polynomial. In this paper we find rational functions w m ( v ) such that for m = 0, 1, 2, …σ m + 1( n )=( − 1 )m + 1w m ( ( 2 n + 1 ) / 2 ) .