Suppose $a\in R^n$, $a \neq 0$, $p > 0$.Calculate $$ \int_{R^n} |xa|^p e^{-||x||^2}dx_1dx_2\cdots dx_n $$ $$xa=x_1a_1+x_2a_2+\cdots+x_na_n$$ I tried to use the following methods:let $y_1=x_1a_1+x_2a_2+\cdots+x_na_n,y_2=x_2,y_3=x_3,\cdots,y_n=x_n$,but I failed. I think it may be related to Gamma Funtion.
2026-04-03 08:17:20.1775204240
Question on a mutiple improper integral
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