Formal power series

Combinatorics

Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012

Walter D. Wallis

The expression “formal power series” is understood to mean that we do not evaluate the power series at any point, or concern ourselves with the question of convergence necessarily. Indeed, some uses of generating functions do not require infinite series at all; in this case, we shall assume that an = 0 for all n greater than some specific integer N.

The directional anti-derivative about a point: existence conditions and some applications

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Journal Information

Published in International Journal of Control, 2023

Laura Menini, Corrado Possieri, Antonio Tornambe

Let be the set of all functions analytic at x = 0, i.e. such that, for each x in a neighbourhood of 0, the series (2) is convergent and its sum is equal to . Clearly, . A formal power series in x is given by the formal sum where ; let be the set of all formal power series in x. A subscript d denotes the functions that in the considered set are d-flat. the set of smooth d-flat functions. If is a set of functions, then is the set of vector functions with entries in . n-dimensional formal power series.

Fibonacci and Lucas Riordan arrays and construction of pseudo-involutions

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Journal Information

Published in Applicable Analysis, 2021

Candice Marshall, Asamoah Nkwanta

Let be the set of all formal power series such that . is a known group under multiplication [16].

Formal power series

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Combinatorics

The directional anti-derivative about a point: existence conditions and some applications

Fibonacci and Lucas Riordan arrays and construction of pseudo-involutions