Talk:Sine Integral Function of Zero

trivial
Sine integral function is already defined as $\map \Si 0 = 0$. --Fake Proof (talk contribs) 01:30, 8 October 2021 (UTC)
 * Perhaps, then, it does not need to be defined specifically at zero. It is here, because the original contributor defined it that way, based probably on . All other sources I've seen do not do this, they just give the main form.


 * It seems apparent that you do not actually need to quote the result at zero. However, none of the source works I've studied actually give the full details. I will hunt around and see whether any of the books on my shelves actually go into the details of the analysis of this function. --prime mover (talk) 05:08, 8 October 2021 (UTC)


 * I have amended the page Definition:Sine Integral Function so as to address this. Thoughts? --prime mover (talk) 12:42, 8 October 2021 (UTC)


 * I suggest $\ds \map \Si x = \int_{t \mathop \to 0}^{t \mathop \to x} \frac {\sin t} t \rd t$. --Fake Proof (talk contribs) 06:19, 9 October 2021 (UTC)


 * Why $t \to x$? Can't we just use $t = x$?


 * I'm not sure whether the improper integral on the half-open interval can be defined at $x = 0$. --Fake Proof (talk contribs) 00:00, 10 October 2021 (UTC)