The tag has no wiki summary.

learn more… | top users | synonyms

9
votes
3answers
2k views

Showing a matrix is negative definite [formerly Showing a sum is always positive]

For each $d$, I have a matrix $M$ with values $$ M_{ij} = \begin{cases} \frac{4ij}{d} - \binom{2d}{d} & i \neq j & \\\\ \frac{4i^2}{d} - \binom{2d}{d} - ...
11
votes
5answers
869 views

Asymptotics of a Bernoulli-number-like function

Tony Lezard asked me the following question which seemed like it should not be too hard but which I did not immediately see how to answer. Define $f(n,k)$ recursively by $f(1,k) = 1$ and $$f(n,k) = ...
2
votes
3answers
511 views

Variant of binomial coefficients

I've recently come across a variant of the binomial polynomials, and I'm curious if anyone has seen these before. If so, I'd love a reference, a name, etc. First recall the following. If z is a ...