Logarithmic integrals with applications to BBP and Euler-type sums

DOI10.1007/S40840-023-01485-3arXiv2302.06640MaRDI QIDQ6426353

Necdet Batir

Publication date: 13 February 2023

Abstract: For real numbers $p,q>1$ we consider the following family of integrals: �egin{equation*} int_{0}^{1}frac{(x^{q-2}+1)logleft(x^{mq}+1 ight)}{x^q+1}{ m d}x quad mbox{and}quad int_{0}^{1}frac{(x^{pt-2}+1)logleft(x^t+1 ight)}{x^{pt}+1}{ m d}x. end{equation*} We evaluate these integrals for all $minmathbbN$, $q=2,3,4$ and $p=2,3$ explicitly. They recover some previously known integrals. We also compute many integrals over the infinite interval $[0,infty)$. Applying these results we offer many new Euler- BBP- type sums.

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Special sequences and polynomials (11B83) Hurwitz and Lerch zeta functions (11M35) Antidifferentiation (26A36)

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