TL;DR
This paper introduces a new class of harmonic-like rational numbers, explores their mathematical properties, and demonstrates their applications in power series expansions and binomial coefficient reciprocals.
Contribution
It defines a novel class of harmonic-like numbers and investigates their relationships with special functions and binomial coefficient reciprocals.
Findings
Established a new class of harmonic-like numbers.
Connected these numbers to power series expansions.
Linked the numbers to reciprocals of binomial coefficients.
Abstract
We define a class of rational numbers including, as a particular case, the classical harmonic numbers. For one particular instance we apply it to the expansion into powers series of a special function, and also detail its relashionship with the reciprocals of the binomial coefficients
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Taxonomy
TopicsMathematical functions and polynomials · Advanced Mathematical Identities · Advanced Mathematical Theories and Applications