Express a function with power-of-k in a polynomial form

Question

I want to express a function $\left(\sum\limits_{i=1}^{n}x_i\right)^{k}$, where $n$ is an arbitrary positive integer and $k$ is an arbitrary positive real number. Is it any way to find out how to express the coefficient of $x_i$? Thanks a lot!

score 1 · Accepted Answer · edited Apr 13 '17 at 12:20

1

Yes, it is the so-called multinomial formula, which is an easy generalization of the formula for $(a+b)^n$.

I could copy here the formula, but it is better if you read the appropriate wikipedia page.

In this thread I explained how to get the case $(a+b+c)^n$.

edited Apr 13 '17 at 12:20

Community

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answered Feb 15 '16 at 12:00

Giovanni Resta

2,368

Express a function with power-of-k in a polynomial form

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