Hey MHF i need some help with this proof.
If\(\displaystyle f(g)= t^m\) and \(\displaystyle g(t)= t^n\), where m and n are positive integers, show that:
\(\displaystyle (f*g)(t)= t^{m+n+1} \int_0^1 \! u^m(1-u)^n \, du.\)
show : \(\displaystyle \int_0^1 \! u^m(1-u)^n \, du = \frac{m!n!}{(m+n+1)!}\)
If\(\displaystyle f(g)= t^m\) and \(\displaystyle g(t)= t^n\), where m and n are positive integers, show that:
\(\displaystyle (f*g)(t)= t^{m+n+1} \int_0^1 \! u^m(1-u)^n \, du.\)
show : \(\displaystyle \int_0^1 \! u^m(1-u)^n \, du = \frac{m!n!}{(m+n+1)!}\)