13 Jun
2020
13 Jun
'20
3:11 p.m.
Lisp (expt 0 0) returns 1. Brent On 6/13/2020 12:27 PM, Andres Valloud wrote:
Your example says 0^0 = binomial(0,0) = number of ways to choose zero apples from a bag with zero apples = 1.
All this of course over the integers.
It came in really handy when proving that
\sum_{k \geq 0} \binom{2k}{k} x^k = \frac{1}{\sqrt{1-4x}}
for | x | < 1/4, via complex calculus. I would have had to excuse the case x = 0, but with 0^0 defined as 1 it's simpler.
Andres.
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