This paper continues investigations on various integral transforms of the Minkowski question mark function. In this work we finally establish the long-sought formula for the moments, which does not explicitly involve regular continued fractions, though it has a hidden nice interpretation in terms of semi-regular continued fractions. The proof is self-contained and does not rely on previous results by the author.
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An extensive bibliography on the Minkowski question mark function. Available at http://www.alkauskas.puslapiai.lt/minkowski.htm
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The author gratefully acknowledges support from the Austrian Science Fund (FWF) under the project Nr. P20847-N18.
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Alkauskas, G. Semi-regular continued fractions and an exact formula for the moments of the Minkowski question mark function. Ramanujan J 25, 359–367 (2011). https://doi.org/10.1007/s11139-011-9307-0
- The Minkowski question mark function
- Moments of distribution
- Bessel functions
- Semi-regular continued fractions
- The Farey tree
Mathematics Subject Classification (2000)