Physics – Mathematical Physics
Scientific paper
2004-02-14
J.Math.Phys.34:1143,1993
Physics
Mathematical Physics
7 pages
Scientific paper
10.1063/1.530189
Power series are introduced that are simultaneously convergent for all real and p-adic numbers. Our expansions are in some aspects similar to those of exponential, trigonometric, and hyperbolic functions. Starting from these series and using their factorial structure new and summable series with rational sums are obtained. For arguments $x\in {\mathbb Q}$ adeles of series are constructed. Possible applications at the Planck scale are also considered.
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