Fractional moments

  title={Fractional moments},
  author={'Oscar Ciaurri},
  journal={Integral Transforms and Special Functions},
  • 'Oscar Ciaurri
  • Published 22 October 2021
  • Mathematics
  • Integral Transforms and Special Functions
We evaluate the moments of some functions composed with the fractional part of 1/x. We name them fractional moments. In particular, we obtain expressions for the fractional moments of some trigonometric functions, the Bernoulli polynomials and the functions x and x(1− x). 
1 Citations
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The paper is about calculating in closed form the following multiple fractional part integral where , are integers and denotes the fractional part of x. We prove that the integral can be expresses in
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I wanted to find an idea that was easier than L’Hospital’s rule and Trigonometric identities forsolving limits approaching zero because it is often very hard to solve these limits with existingideas.