MathOverflow

This is a continuation of the previous Question 508825.
Let$$g(k,\varepsilon)=\frac{1}{(k+\varepsilon)^2(k-\varepsilon)^2\binom{2 k}{k+\varepsilon}},$$and$$G^{(n)}(k)=\frac{\partial^{n}}{\partial \varepsilon^{n}}g(k,\varepsilon)\biggr|_{\varepsilon=0}.$$I discovered the following identities...

Suppose $U\subseteq\mathbb C$ is a connected open set, and $f:U\to\mathbb C$ is a function whose partial derivatives in the first and second components exist and are continuous on $U$. It is well-known that $f$ is analytic if and only if $f$ satisfies...

Let X be a space, viewed as an infinity-groupoid. Suppose one has a functor
F : X^op -> Cat^perf_infinity,
where Cat^perf_infinity denotes the infinity-category of small idempotent-complete stable infinity-categories and exact functors.

The bar construction is a standard way of generating an interesting chain complex from some sort of algebraic data. In some work I'm doing, I've encountered a variant of the bar construction where roughly speaking entries of the generators have a circular...