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Let \(n\in\mathbb N\). For\[e^xf_n(x)=\sum_{k=1}^\infty\frac{k^nx^k}{\left(k1\right)!}\]show that \(f_n(x)\) is a polynomial of degree \(n+1\) with integer coefficients.
Tricky question.
 one year ago
 one year ago
Let \(n\in\mathbb N\). For\[e^xf_n(x)=\sum_{k=1}^\infty\frac{k^nx^k}{\left(k1\right)!}\]show that \(f_n(x)\) is a polynomial of degree \(n+1\) with integer coefficients. Tricky question.
 one year ago
 one year ago

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badreferencesBest ResponseYou've already chosen the best response.1
@TuringTest @KingGeorge @Zarkon You guys might be interest.
 one year ago

badreferencesBest ResponseYou've already chosen the best response.1
@bahrom7893 You too, maybe lol.
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
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
 one year ago

bahrom7893Best ResponseYou've already chosen the best response.0
no im most likely not interested lol
 one year ago

bahrom7893Best ResponseYou've already chosen the best response.0
Anyway... I'm off for tonight guys, interviews in 10 hrs. I need my sleep. Gnite eastern front.
 one year ago

badreferencesBest ResponseYou've already chosen the best response.1
Cheers, good luck. Don't dead.
 one year ago

badreferencesBest ResponseYou've already chosen the best response.1
You can ignore the sub. It's just a marker to show that the function \(f\) is dependent on \(n\).
 one year ago

perlBest ResponseYou've already chosen the best response.0
well first lets look at e^x, whats the series of this
 one year ago

badreferencesBest ResponseYou've already chosen the best response.1
You don't have to walk me through it, lol, I already have the solution. This is just a very difficult challenge.
 one year ago

perlBest ResponseYou've already chosen the best response.0
e^x dw:1348817638823:dw
 one year ago

perlBest ResponseYou've already chosen the best response.0
so we can see immediately that
 one year ago

badreferencesBest ResponseYou've already chosen the best response.1
I'll post it when I can pick it up, Sir, it's not in my possession right now.
 one year ago

mukushlaBest ResponseYou've already chosen the best response.0
see if this is right or not http://openstudy.com/study#/updates/50651902e4b08d185211d536
 one year ago

mukushlaBest ResponseYou've already chosen the best response.0
i proved that\[f_1(x)=x+x^2\]and\[f_{n+1}(x)=x(f_n(x)+f_n^'(x))\]
 one year ago

badreferencesBest ResponseYou've already chosen the best response.1
Full solution. I can't seem to attach the .ps file so I did a screencap with ghostview,
 one year ago
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