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badreferences
 3 years 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.
badreferences
 3 years 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.

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badreferences
 3 years ago
Best ResponseYou've already chosen the best response.1@TuringTest @KingGeorge @Zarkon You guys might be interest.

badreferences
 3 years ago
Best ResponseYou've already chosen the best response.1@bahrom7893 You too, maybe lol.

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.0I 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

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0no im most likely not interested lol

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0Anyway... I'm off for tonight guys, interviews in 10 hrs. I need my sleep. Gnite eastern front.

badreferences
 3 years ago
Best ResponseYou've already chosen the best response.1Cheers, good luck. Don't dead.

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

perl
 3 years ago
Best ResponseYou've already chosen the best response.0well first lets look at e^x, whats the series of this

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

perl
 3 years ago
Best ResponseYou've already chosen the best response.0so we can see immediately that

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

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

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

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