Prove that, for any function $f(x)$,
\[ \frac{{d^{n}}}{{dx^{n}}}f(x)=\lim_{h\to 0}\frac{\sum_{i=0}^{n}{(-1)^{i}}\binom{n}{i}f(x+(n-i)h)}{h^{n}} \]
N'th Differencial
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Re: N'th Differencial
Is it your own problem? I'd like to request everyone to write a few words about the source of the problem. (You should hide the sources in some cases)
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Re: N'th Differencial
অামার প্রবলেম বলতে নিজেই বের করসি, কিন্তু অাগেও নিশ্চয় কেউ বের করসে।
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- zadid xcalibured
- Posts:217
- Joined:Thu Oct 27, 2011 11:04 am
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Re: N'th Differencial
Induction and combinatorial argument both yeilds easy solution.