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Euler’s factorial series and global relations. (English) Zbl 1444.11037
Summary: Using Padé approximations to the series \(E(z) = \sum_{k = 0}^\infty k!(- z)^k\), we address arithmetic and analytical questions related to its values in both \(p\)-adic and Archimedean valuations.

11B65 Binomial coefficients; factorials; \(q\)-identities
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
41A21 Padé approximation
33E50 Special functions in characteristic \(p\) (gamma functions, etc.)
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