Symbolic solutions of some linear recurrences
E. Di Nardo, D. Senato
TL;DR
This paper introduces a symbolic method for solving linear recurrence relations using polynomial sequences represented as moments of a symbol, applicable to combinatorial and statistical problems, and provides explicit solutions for Sheffer sequences.
Contribution
It presents a novel symbolic approach to solving linear recurrences, connecting polynomial sequences with moments of a symbol without probability spaces.
Findings
Explicit form for Sheffer sequence recurrences
Method applicable to combinatorial and statistical sequences
Easy implementation in symbolic software
Abstract
A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of polynomial sequences as moments of a symbol that looks as the framework of a random variable with no reference to any probability space. We give several examples of applications and state an explicit form for the class of linear recurrences involving Sheffer sequences satisfying a special initial condition. The results here presented can be easily implemented in a symbolic software.
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