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  4. The Formulas for Sum of Products of Sequences Associated With the Metallic Means

The Formulas for Sum of Products of Sequences Associated With the Metallic Means

CDS.
2020;
Volume 1, Number 1
: pp. 73 - 78
https://doi.org/10.23939/cds2020.01.073
Authors:
  1. P. Kosobutskyi
  2. N. Nestor
1
Lviv Polytechnic National University, Ukraine
2
Lviv Polytechnic National University

In this paper, the regularities of convolution of sequences c of Fibonacci numbers {Fn} generated by metallic means and the sum of products of two statistically independent sequences {Fi} and Jn=j∙sin(0.5π(n-j)) are investigated. It is shown that the known closed forms of sums for convolutionn ... and product ...
are similar. Attention to the study of the convolution of two sequences of discrete data is associated with the use of this method for statistical signal processing. This problem involves calculating finite sums as discrete analogs of definite integrals. Such a problem is considered solved if the formula for the sum is expressed in a closed form as a function of its members and their number.

Golden ratio
metallic meаns
Fibonacci sequences
the roots of the quadratic equation
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