Umbral Methods and Harmonic Numbers
Giuseppe Dattoli, Bruna Germano, Silvia Licciardi, Maria Renata, Martinelli
TL;DR
This paper explores harmonic-based functions using umbral operational methods, deriving new results through elementary Gaussian integral properties to deepen understanding of harmonic numbers.
Contribution
It introduces novel applications of umbral methods to harmonic functions, expanding the theoretical framework with new derivations.
Findings
Derived new identities involving harmonic numbers
Applied Gaussian integrals to harmonic function analysis
Extended umbral methods to harmonic number theory
Abstract
The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
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