Xrfgtjtk

.mw-parser-output .infobox{border:1px solid #aaa;background-color:#f9f9f9;color:black;margin:.5em 0 .5em 1em;padding:.2em;float:right;clear:right;width:22em;text-align:left;font-size:88%;line-height:1.6em}.mw-parser-output .infobox td,.mw-parser-output .infobox th{vertical-align:top;padding:0 .2em}.mw-parser-output .infobox caption{font-size:larger}.mw-parser-output .infobox.bordered{border-collapse:collapse}.mw-parser-output .infobox.bordered td,.mw-parser-output .infobox.bordered th{border:1px solid #aaa}.mw-parser-output .infobox.bordered .borderless td,.mw-parser-output .infobox.bordered .borderless th{border:0}.mw-parser-output .infobox-showbutton .mw-collapsible-text{color:inherit}.mw-parser-output .infobox.bordered .mergedtoprow td,.mw-parser-output .infobox.bordered .mergedtoprow th{border:0;border-top:1px solid #aaa;border-right:1px solid #aaa}.mw-parser-output .infobox.bordered .mergedrow td,.mw-parser-output .infobox.bordered .mergedrow th{border:0;border-right:1px solid ...

0 $begingroup$ I am reading the book Introduction to Cyclotomic Fields. I found the following limit on page number 33. I have no idea how to obtain the following limit. $$lim_{xto 1-n} (e^{(2 pi i x)}-1)Gamma(x)=frac{(2pi i)(-1)^{(n-1)}}{(n-1)!}.$$ Do we need to use L'Hospital's rule for this? Is there any connection with the residue of Gamma function at negative values? The residue at $z=k$ is given by $operatorname{Re}s_{z=k} Gamma(z)=frac{(-1)^{k}}{k!}.$ Please help me to understand this. complex-analysis number-theory limits gamma-function share | cite | improve this question edited Dec 18 '18 at 21:09 ...