Commit 2024-09-28 23:34 d453819b

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feat: the real exponential is analytic (#17218) Currently, mathlib proves that the complex exponential is analytic as a consequence of its differentiability, quite late in the import hierarchy -- and this is specific to complexes. On the other hand, we also know that the exponential on a general normed algebra is analytic, thanks to its power series expansion. We switch to deduce the former from the latter, earlier in the import hierarchy, and use this occasion to also prove analyticity of the real exponential in the same file.

Estimated changes

added theorem AnalyticAt.cexp
added theorem AnalyticAt.rexp
added theorem AnalyticOn.cexp
added theorem AnalyticOn.rexp
added theorem AnalyticOnNhd.cexp
added theorem AnalyticOnNhd.rexp
added theorem AnalyticWithinAt.cexp
added theorem AnalyticWithinAt.rexp
modified theorem Complex.contDiff_exp
modified theorem Real.contDiff_exp
modified theorem Real.differentiableAt_exp
added theorem analyticAt_cexp
added theorem analyticAt_rexp
added theorem analyticOnNhd_cexp
added theorem analyticOnNhd_rexp
added theorem analyticOn_cexp
added theorem analyticOn_rexp