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Power series are introduced that are simultaneously convergent for all realand p-adic numbers. Our expansions are in some aspects similar to those ofexponential, trigonometric, and hyperbolic functions. Starting from theseseries and using their factorial structure new and summable series withrational sums are obtained. For arguments $x\in {\mathbb Q}$ adeles of seriesare constructed. Possible applications at the Planck scale are also considered.Comment: 7 page

Power series everywhere convergent on R and all Qp