What is $e, \pi, \ln 2,...$ etc in p adic? And how to flip digits of decimal points? Does p-adic have their own constants? 10 adic base.
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Could anyone give the first (or last, with p-adic it's hard to know what language to use) few digits for an example? Perhaps even a possible sequence that describes e. – alan2here Aug 07 '17 at 20:06
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Related: https://math.stackexchange.com/q/4213789/96384 – Torsten Schoeneberg Oct 03 '22 at 01:25
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The $p$-adic logarithm function and $p$-adic exponential function have been defined. The value of $\ln 2$ can be worked out, although it's a little tricky. The value of $e$ itself can't be worked out, I don't think - the series doesn't converge there - but $e^p$ can, for example.
I don't know if there is a $p$-adic analogue of $\pi$.
Greg Martin
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This mathoverflow answer claims that there's a $p$-adic analogue of $2\pi i$. I have my doubts it's what the OP is looking for, but it's the best thing I can remember to a $p$-adic analogue of $\pi$. – Mar 26 '14 at 07:58
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1It's possible that the OP meant to ask about the $p$-ary decimal-like expansions of these constants, in which case yes, all real numbers have such expansions in any base, prime or not. – Greg Martin Mar 26 '14 at 17:58
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