Talk:Polynomial expansion

Pascals Triangle

The coeffecients of all the terms are highly dependent on the appropriate line of pascal's triangle. This should be included in the article. 202.168.18.88 02:23, 21 October 2007 (UTC)

Using the terms degree, power

I'm not a native English speaker and unsure about this. But I think the terms degree and power are used as follows…

• x has degree y; x is of degree y
• x is raised to the power of y

…while the article mixes both formulations:

• variables raised to different degrees

Could someone please rephrase the article in case I'm right here? Thank you. — Ocolon 18:07, 21 March 2007 (UTC)

Question that had been posted on the article page, moving here, not sure if a solution to the question below belongs in this article

How to solve the problem: turn production-sum into sum-production $\prod _{n}\left(\sum _{m}A_{mn}\right)=\sum _{m}\left(\prod _{n}B_{mn}\right)$, What is $B_{mn}$ in terms of $A_{mn}$? —Preceding unsigned comment added by 206.169.234.26 (talk) 21:50, 30 June 2010 (UTC)

A good question, even if not directly related to this article. To write the expansion in a clear form we have to use more structured set than just $\{1,2,\dots ,m\}$ as index sets. Let $I$ and $J$ be finite sets, and let $J^{\,I}$ be the set of all functions $\mu :I\to J$. Then

$\prod _{n\in I}\sum _{m\in J}a_{n,m}=\sum _{\mu \in J^{I}}\prod _{n\in I}a_{n,\mu (n)}.$

--pma 07:10, 1 May 2011 (UTC)