Binomial Theorem
From QED
In the discrete case, the Binomial Theorem is
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where is the binomial coefficient .
which may be proven with induction.
In the case continuous case, where r is any complex number and | x / y | < 1, or r is a positive integer,
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Where :
Which may be proven by taking the power series of the left hand expression.
As useful form of this holds for the reciprocal power
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Which the geometric series is a special case of when r = 1.
This page was recovered in October 2009 from the Plasmagicians page on Binomial_Theorem dated 06:05, 16 October 2006.