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On combinatorial functions related to the Bürman-Lagrange series. Quasi-orthogonality relations

On combinatorial functions related to the Bürman-Lagrange series. Quasi-orthogonality relations -- Let II=HI be a formal power series (f.p.s.) over the field of real or complex numbers. In connection with the B rman-Lagrange series, it is useful to consider the quantities Coef,,-*[fV"""«)], n =1,2 ..... k = l ..... n, which were introduced by the author and for m = 1 coincide with the /^-functions introduced by M. L. Platonov. Using Henrici's method, we show that the set of quantities Q(m\n,k) = - Coef ,*[/""(/)], k\ n = 1,2,..., k = 1, ...,/, forms a quasi-orthogonal to the set {/^(,)}, n = 1,2,..., k = 1, ...,n. We describe some properties of the coefficients of the series jcf(r), the rth power of a f.p.s. x(t) over the field K, where r e K. This research was supported by the Russian Foundation for Basic Research, grant 96-01-00531. INTRODUCTION Let K be the field of real or complex numbers and let K[t] be the algebra of formal power series (f.p.s.) over the field K. If ~~ ,-> £**(>, m>l, (1.1) is an element of K[t], then, as it is shown in the next section, there exists a f.p.s. [t~mg(t)]~n/m e K(t), the (-n/m)th power of the series t~mg(t). We consider http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Discrete Mathematics and Applications de Gruyter

On combinatorial functions related to the Bürman-Lagrange series. Quasi-orthogonality relations

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References (15)

Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0924-9265
eISSN
1569-3929
DOI
10.1515/dma.1998.8.1.53
Publisher site
See Article on Publisher Site

Abstract

-- Let II=HI be a formal power series (f.p.s.) over the field of real or complex numbers. In connection with the B rman-Lagrange series, it is useful to consider the quantities Coef,,-*[fV"""«)], n =1,2 ..... k = l ..... n, which were introduced by the author and for m = 1 coincide with the /^-functions introduced by M. L. Platonov. Using Henrici's method, we show that the set of quantities Q(m\n,k) = - Coef ,*[/""(/)], k\ n = 1,2,..., k = 1, ...,/, forms a quasi-orthogonal to the set {/^(,)}, n = 1,2,..., k = 1, ...,n. We describe some properties of the coefficients of the series jcf(r), the rth power of a f.p.s. x(t) over the field K, where r e K. This research was supported by the Russian Foundation for Basic Research, grant 96-01-00531. INTRODUCTION Let K be the field of real or complex numbers and let K[t] be the algebra of formal power series (f.p.s.) over the field K. If ~~ ,-> £**(>, m>l, (1.1) is an element of K[t], then, as it is shown in the next section, there exists a f.p.s. [t~mg(t)]~n/m e K(t), the (-n/m)th power of the series t~mg(t). We consider

Journal

Discrete Mathematics and Applicationsde Gruyter

Published: Jan 1, 1998

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