Fractional moments

@article{Ciaurri2022FractionalM,
  title={Fractional moments},
  author={{\'O}scar Ciaurri},
  journal={Integral Transforms and Special Functions},
  year={2022},
  volume={33},
  pages={766 - 781}
}
  • Ó. 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 call them fractional moments. In particular, we obtain expressions for the fractional moments of some trigonometric functions, the Bernoulli polynomials and the functions and . 
1 Citations

On expansions involving the Riemann zeta function and its derivatives

References

SHOWING 1-10 OF 13 REFERENCES

The evaluation of a class of fractional part integrals

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

Representation of a class of multiple fractional part integrals and their closed form

ABSTRACT In this paper, the following generalized multiple fractional part integrals: and are considered for complex numbers , positive integers and positive number a, where denotes the fractional

Exotic fractional part integrals and Euler´s constant

Abstract The paper is about calculating single integrals of the form ∫01xm{1/x}kdx and double fractional part integrals of the form ∫01∫01{x/y}m{y/x}kdxdy, where m,k, are nonnegative integers. In

On Some Integrals Involving the Hurwitz Zeta Function: Part 2

AbstractWe establish a series of indefinite integral formulae involving the Hurwitz zeta function and other elementary and special functions related to it, such as the Bernoulli polynomials, ln

Old and New Identities for Bernoulli Polynomials via Fourier Series

TLDR
The Fourier coefficients of any polynomial restricted to and extended by periodicity are linear combinations of terms of the form and by uniqueness of Fourier series, a relation between the given family and the Bernoulli polynomials is obtained.

A Table of Integrals

Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + b dx = 1 a ln |ax + b| (4) Integrals of Rational Functions 1 (x + a) 2 dx = −

Concrete mathematics - a foundation for computer science

From the Publisher: This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid