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 2005: Roland E. Larson, Robert P. Hostetler and Bruce H. Edwards: Calculus (8th ed.). 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)