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Abstract
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
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AMS CLASSIFICATIONs:
Disclosure statement
No potential conflict of interest was reported by the author.
Notes
1 This fact follows from (Equation4.4(4.4) ) applying the identity
which can be proved by using the exponential generating function
Additional information
Funding
The author was supported by grant PGC2018-096504-B-C32 Agencia Estatal de Investigación (AEI), from Spanish Government.