Recursive Harmonic Numbers and Binomial Coefficients
Aung Phone Maw, Aung Kyaw
TL;DR
This paper introduces recursive harmonic numbers as a new generalization of harmonic numbers, explores their structure through a Pascal-like table, and derives a formula involving binomial coefficients.
Contribution
It presents the concept of recursive harmonic numbers, constructs their table, and provides a binomial coefficient formula, advancing harmonic number theory.
Findings
Recursive harmonic numbers generalize harmonic numbers.
A Pascal-like table for recursive harmonic numbers is constructed.
A formula involving binomial coefficients for recursive harmonic numbers is derived.
Abstract
We define recursive harmonic numbers as a generalization of harmonic numbers. The table of recursive harmonic numbers, which is like Pascal's triangle, is constructed. A formula for recursive harmonic numbers containing binomial coefficients is also presented.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Mathematics and Applications