# Difference between revisions of "User talk:PaoloMartini"

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PaoloMartini (talk | contribs) |
PaoloMartini (talk | contribs) |
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:<math>p(x-1) = \sum_{i=0}^n a_i (x - 1)^i |
:<math>p(x-1) = \sum_{i=0}^n a_i (x - 1)^i |
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− | = \sum_{i=0}^n \left[ a_i \left( \sum_{k=0}^n {n \choose k} x^k (-1)^k \right) \right] |
+ | = \sum_{i=0}^n \left[ a_i \left( \sum_{k=0}^n {n \choose k} x^k (-1)^k \right) \right] |

+ | = \sum_{i=0}^n \sum_{k=0}^i (-1)^k a_i {n \choose k} x^k</math> |
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zZzZ... |
zZzZ... |

## Revision as of 17:29, 14 September 2006

Show that if is a polynomial of degree , then is a polynomial of the same degree.

Definition of polynomial.

Binomial theorem.

Special case.

Binomial coefficient simmetry.

Hence:

zZzZ...