I am wondering how to evaluate $$\int_0^t(t-s)^{-a}\sin(t-s)ds$$ for $a>0$. If $a=1$ this is just the sine integral. Is there some way of doing it for a variable $a$? I plugged it in to the WolframAlpha integrator and it gave me the gamma function, $$\frac{i}{2}[ \Gamma(1-a,i(s-t)) - \Gamma(1-a,i(t-s))]\Bigr|_{s=0}^t $$ but I think this is wrong because the first argument of the incomplete gamma function has to be a positive integer.
2026-05-05 05:21:10.1777958470
How to evaluate this integral for variable $a$?
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