- #1
heinerL
- 19
- 0
Hey
i stumbled over a problem which i can't solve:
f is a continuous function on [a,b] and F_n is recursive given through:
[tex]F_1(x)=\int_a^x f(t) \ dt[/tex]
and
[tex]F_{n+1}=\int_a^x F_n(t) \ dt[/tex]
I have to proof that F_n looks like this:
[tex]F_n(x)=\frac{1}{(n-1)!}\int_a^x (x-t)^{n-1} f(t) \ dt[/tex]
For n=1 it's no big deal but then i have no clue. I think it must have something to do with differentiation under the integral sign because that's where i found it.
Hope anybody can help me! thx
i stumbled over a problem which i can't solve:
f is a continuous function on [a,b] and F_n is recursive given through:
[tex]F_1(x)=\int_a^x f(t) \ dt[/tex]
and
[tex]F_{n+1}=\int_a^x F_n(t) \ dt[/tex]
I have to proof that F_n looks like this:
[tex]F_n(x)=\frac{1}{(n-1)!}\int_a^x (x-t)^{n-1} f(t) \ dt[/tex]
For n=1 it's no big deal but then i have no clue. I think it must have something to do with differentiation under the integral sign because that's where i found it.
Hope anybody can help me! thx