## badreferences Group Title Let $$n\in\mathbb N$$. For$e^xf_n(x)=\sum_{k=1}^\infty\frac{k^nx^k}{\left(k-1\right)!}$show that $$f_n(x)$$ is a polynomial of degree $$n+1$$ with integer coefficients. Tricky question. one year ago one year ago

1. badreferences Group Title

@TuringTest @KingGeorge @Zarkon You guys might be interest.

2. badreferences Group Title

@bahrom7893 You too, maybe lol.

3. TuringTest Group Title

I got a linear thingy when I tried it that makes no sense, I'll write my work in a minute just so somebody can laugh at it

4. bahrom7893 Group Title

no im most likely not interested lol

5. bahrom7893 Group Title

Anyway... I'm off for tonight guys, interviews in 10 hrs. I need my sleep. Gnite eastern front.

6. badreferences Group Title

Cheers, good luck. Don't dead.

7. bahrom7893 Group Title

thanks :)

8. perl Group Title

what is f sub n (x) ?

9. badreferences Group Title

You can ignore the sub. It's just a marker to show that the function $$f$$ is dependent on $$n$$.

10. perl Group Title

well first lets look at e^x, whats the series of this

11. badreferences Group Title

You don't have to walk me through it, lol, I already have the solution. This is just a very difficult challenge.

12. perl Group Title

e^x |dw:1348817638823:dw|

13. perl Group Title

so we can see immediately that

14. perl Group Title

|dw:1348817750800:dw|

15. perl Group Title

whats solution

16. badreferences Group Title

I'll post it when I can pick it up, Sir, it's not in my possession right now.

17. perl Group Title

ohhh

18. perl Group Title

darn

19. perl Group Title

we know that

20. perl Group Title

|dw:1348817984611:dw|

21. mukushla Group Title

see if this is right or not http://openstudy.com/study#/updates/50651902e4b08d185211d536

22. mukushla Group Title

i proved that$f_1(x)=x+x^2$and$f_{n+1}(x)=x(f_n(x)+f_n^'(x))$

23. badreferences Group Title

Full solution. I can't seem to attach the .ps file so I did a screencap with ghostview,