For what $g\equiv g(r,q)$ such that following is true: $$ \int_0^\infty r^{2n-1}g(r,q)dr=\frac{\Gamma(qn+1)}{n^2}. $$ The function $g$ should be independent of $n$. It can only have $r$ and $q$.
Asked
Active
Viewed 35 times
1
-
What is the context for this problem? What have you tried to solve it? – Aaron Mar 12 '21 at 20:12
-
We individually know the structure of $g$ to get $\Gamma(qn+1)$ and $\frac{1}{n^2}$. But I am trying to combine this in the above format. – HIMANSHU SINGH Mar 13 '21 at 12:12
-
But what makes you think there is such a $g$ to begin with? Is this a homework problem? An exercise in a book? Your own conjecture? Have you made partial progress? Where are you running into difficulties? – Aaron Mar 13 '21 at 15:14