Binomial transform of products
Khristo N. Boyadzhiev
TL;DR
This paper develops methods to compute the binomial transform of the product of two sequences with known transforms, deriving identities and illustrating with examples involving special number sequences and polynomials.
Contribution
It introduces a systematic approach to find the binomial transform of product sequences and provides new identities and examples involving special sequences.
Findings
Derived identities for binomial transforms of product sequences
Provided examples with harmonic, Bernoulli, Fibonacci numbers, and Laguerre polynomials
Enhanced understanding of binomial transform properties for special sequences
Abstract
Given two infinite sequences with known binomial transforms, we compute the binomial transform of the product sequence. Various identities are obtained and numerous examples are given involving sequences of special numbers: Harmonic numbers, Bernoulli numbers, Fibonacci numbers, and also Laguerre polynomials.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Fractal and DNA sequence analysis · Advanced Combinatorial Mathematics