On the Generating Functions of Numerical Sequences
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- k-Fibonacci Numbers, k-Fibonomial Numbers, Generating Function, Recurrence Relation, Convolution, Abelian Field, MSC2000 - 15A36, 11C20, 11B39
- Sergio Falcon
- 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.
Full text: IJISM_945_FINAL.pdf [Bibtex]