Is it true that for complex $s$: $\lim\limits_{s\to 1} \frac{2-2^s}{s-1}=-2\log (2)$?
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Is it true that for complex $s$,
$$\lim_{s\to 1} \frac{2-2^s}{s-1}=-2\log (2)?$$
If so, prove it.
complex-analysislimits
asked 2011-09-22
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This is a piece of a problem from a Number Thoery book Im working through. I dont know much Complex Analysis. Any suggested books? – 2011-09-22
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Dunno, I've only picked it up here and there. It's possible you could get the fundamentals down through lecture notes and pdfs and Wikipedia and such. Number theory (of the not-elementary sort), especially analytic NT, utilizes complex analysis a lot. – 2011-09-22