A family of summation formulas involving generalized harmonic numbers
Chuanan Wei, Qinglun Yan, Dianxuan Gong
TL;DR
This paper introduces a new family of summation formulas that involve generalized harmonic numbers, derived using a combination of derivative operators and binomial sums through telescoping techniques.
Contribution
It presents novel summation formulas involving generalized harmonic numbers obtained via a unique combination of derivative operators and telescoping binomial sums.
Findings
Derived new summation formulas involving generalized harmonic numbers.
Established connections between derivative operators and binomial sums.
Provided a systematic method for summation involving harmonic numbers.
Abstract
Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Analytic Number Theory Research