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badreferences

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

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

    • one year ago
  2. badreferences
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    @bahrom7893 You too, maybe lol.

    • one year ago
  3. TuringTest
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    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
  4. bahrom7893
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    no im most likely not interested lol

    • one year ago
  5. bahrom7893
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    Anyway... I'm off for tonight guys, interviews in 10 hrs. I need my sleep. Gnite eastern front.

    • one year ago
  6. badreferences
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    Cheers, good luck. Don't dead.

    • one year ago
  7. bahrom7893
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    thanks :)

    • one year ago
  8. perl
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    what is f sub n (x) ?

    • one year ago
  9. badreferences
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    You can ignore the sub. It's just a marker to show that the function \(f\) is dependent on \(n\).

    • one year ago
  10. perl
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    well first lets look at e^x, whats the series of this

    • one year ago
  11. badreferences
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    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
  12. perl
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    e^x |dw:1348817638823:dw|

    • one year ago
  13. perl
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    so we can see immediately that

    • one year ago
  14. perl
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    |dw:1348817750800:dw|

    • one year ago
  15. perl
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    whats solution

    • one year ago
  16. badreferences
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    I'll post it when I can pick it up, Sir, it's not in my possession right now.

    • one year ago
  17. perl
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    ohhh

    • one year ago
  18. perl
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    darn

    • one year ago
  19. perl
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    we know that

    • one year ago
  20. perl
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    |dw:1348817984611:dw|

    • one year ago
  21. mukushla
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    see if this is right or not http://openstudy.com/study#/updates/50651902e4b08d185211d536

    • one year ago
  22. mukushla
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    i proved that\[f_1(x)=x+x^2\]and\[f_{n+1}(x)=x(f_n(x)+f_n^'(x))\]

    • one year ago
  23. badreferences
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    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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