Armin Straub, Wadim Zudilin — International Mathematics Research Notices — Volume 2023, Number 11, 2023, Pages 9861-9879
Abstract
We explicitly determine the Apéry limits for the sums of powers of binomial coefficients. As an application, we prove a weak version of Franel's conjecture on the order of the recurrences for these sequences. Namely, we prove the conjectured minimal order under the assumption that such a recurrence can be obtained via creative telescoping.Download
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BibTeX
@article{franel-aperylimits-2023,
author = {Armin Straub and Wadim Zudilin},
title = {Sums of powers of binomials, their Ap\'ery limits, and Franel's suspicions},
journal = {International Mathematics Research Notices},
year = {2023},
volume = {2023},
number = {11},
pages = {9861--9879},
doi = {10.1093/imrn/rnac125},
}