TL;DR
This paper introduces the concept of fractional moments, providing explicit formulas for their calculation across various functions including trigonometric functions, Bernoulli polynomials, and power functions.
Contribution
It offers new explicit expressions for fractional moments of several important classes of functions, expanding the analytical tools available for their study.
Findings
Derived formulas for fractional moments of trigonometric functions
Established expressions for Bernoulli polynomials' fractional moments
Calculated fractional moments for power functions and their products
Abstract
We evaluate the moments of some functions composed with the fractional part of . We name them fractional moments. In particular, we obtain expressions for the fractional moments of some trigonometric functions, the Bernoulli polynomials and the functions and .
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Taxonomy
TopicsMathematical functions and polynomials · Advanced Mathematical Identities · Mathematical Inequalities and Applications