On the Generating Functions of Numerical Sequences

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Year:
2021
Type of Publication:
Article
Keywords:
k-Fibonacci Numbers, k-Fibonomial Numbers, Generating Function, Recurrence Relation, Convolution, Abelian Field, MSC2000 - 15A36, 11C20, 11B39
Authors:
Sergio Falcon
Journal:
IJISM
Volume:
9
Number:
4
Pages:
58-69
Month:
July
ISSN:
2347-9051
Abstract:
In this paper we study the generating function of an integer sequence and its relation with the recurrence relation between the terms of the sequence. We recall some generating functions previously studied and create new ones especially from the convolution of sequences and the derivatives of the initial generating functions. With respect to the sum and the convolution of integer sequences, an abelian field is found. Finally, we study the inverse sequence with respect to the convolution.

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