Masato Kobayashi
Published 2021-08-28Version 1
We show new integral representations for dilogarithm and trilogarithm functions on the unit interval. As a consequence, we also prove (1) new integral representations for Apery, Catalan constants, and Legendre chi functions of order 2, 3, (2) a lower bound for the dilogarithm function on the unit interval, (3) new Euler sums.
On partitions of the unit interval generated by Brocot sequences
One example of singular representations of real numbers from the unit interval
Discrepancy of generalized $LS$-sequences
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