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- W3215072014 abstract "We study p-adic Euler's series Ep(t)=∑k=0∞k!tk at a point pa, a∈Z≥1, and use Padé approximations to prove a lower bound for the p-adic absolute value of the expression cEp(±pa)−d, where c,d∈Z. It is interesting that the same Padé polynomials which p-adically converge to Ep(t), approach the Hardy integral H(t)=∫0∞e−s1−tsds on the Archimedean side. This connection is used with a trick of analytic continuation when deducing an Archimedean bound for the numerator Padé polynomial needed in the derivation of the lower bound for |cEp(±pa)−d|p. Furthermore, we present an interconnection between E(t) and H(t) via continued fractions." @default.
- W3215072014 created "2021-12-06" @default.
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- W3215072014 date "2023-03-01" @default.
- W3215072014 modified "2023-09-25" @default.
- W3215072014 title "Euler's factorial series, Hardy integral, and continued fractions" @default.
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- W3215072014 doi "https://doi.org/10.1016/j.jnt.2022.09.007" @default.
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