Hi, this is a very challenging question.
Please find attached.

Question

Hi, this is a very challenging question.
Please find attached.

anonymous · Answer

attachment

anonymous · Answer

Hi, the first. part. I am able to prove it. just use integration by parts.
x^m and (ln(x))^n will give you the answer.

Can anyone tell me how to do part 2?

math&ing001 · Answer

$$F(m,n)=-\frac{ m }{ n-1 }*F(m,n-1)=-\frac{ m }{ n-1}*(-\frac{ m }{ n-2 })*F(m,n-3)$$
Can you finish it?

anonymous · Answer

awesome. it should be (m)/(n+1) i think

anonymous · Answer

sorry. the numerator is n*(n-1)*(n-2)....all the way down.
denominotor is (m+1)*(m+1).....all the way

math&ing001 · Answer

Yeah sry my bad. Your answer only lacks (-1)^n.
Now what do you think the second step should be?

anonymous · Answer

Like the attached ?

anonymous · Answer

Yes. (-1)^n. thanks for the reminder

math&ing001 · Answer

Yes correct :)

math&ing001 · Answer

Now take it all the way till F(m-n,0)