Artin–Hasse exponential
In mathematics, specifically in p-adic analysis, the Artin–Hasse exponential, introduced by Emil Artin and Helmut Hasse in 1928, is the power series given by E p ( x ) = exp ( x + x p p + x p 2 p 2 + x p 3 p 3 + ⋯ ) . {\displaystyle E_{p}(x)=\exp \left(x+{\frac {x^{p}}{p}}+{\frac {x^{p^{2}}}{p^{2}}}+{\frac {x^{p^{3}}}{p^{3}}}+\cdots \right).} == Motivation == One motivation for considering this series to be analogous to the exponential function comes from infinite products.