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Results tagged with binomial-coefficients
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user 35626
For questions that explicitly reference the binomial coefficients, Pascal's Triangle, and Binomial identities.
0
votes
Maximum value of the binomial coefficient as a polynomial
I'll post a sketch for now, and fill it in later. I use C(x) for $\binom{x}{k}$.
Taking derivative wrt x, I get C(x)(sum 1/(x-i)). Thus local extrema occur when one subsum of fractions equals the …
- 2,158
1
vote
Simplest form for sum of Binomial Expressions
Addendum: I misread the problem, not paying attention to the for all s and r. Thus the trivial
answer to the second more general question trivially misses the intent. However, one can
change the pro …
- 2,158
2
votes
Estimating a sum involving binomial coefficients [refined]
You can rewrite it as $$\frac{(m+q)!}{(m-q)!(q!)^2} \sum_{0\leq i \leq m-q} \frac{\binom{m}{i+q}\binom{m-q}{i}}{\binom{m+q}{i+q}}$$, but if W-Z gives a hypergeometric result as in Dima Pasechnik's an …
- 2,158