# Tagged Questions

Hypergeometric functions are the analytic functions defined by Taylor expansions of the shape $\sum_{n \geq 0} a_n x^n$, where $a_{n+1}/a_n$ is a rational function of $n$. This general family of functions encompasses many classical functions. The hypergeometric functions play an important role in ...

This historical question recalls Pafnuty Chebyshev's estimates for the prime distribution function. In his derivation Chebyshev used the factorial ratio sequence $$u_n=\frac{(30n)!n!}{(15n)!(10n)!(6n)... 5answers 3k views ### Groups, quantum groups and (fill in the blank) In the study of special functions there are three levels of objects, classical, basic and elliptic. These correspond to classical hypergeometric functions, basic (q-) hypergeometric functions, and ... 0answers 408 views ### Relation between two hypergeometric series EDIT: Context for this investigation can be found in one of my other MO posts, "Pythagorean Theorem for Right-Corner Hyperbolic Simplices?" -- I'm investigating a function that has led me to this ... 0answers 143 views ### a variational problem related to weighted logarithmic capacity Consider the following multiple contour integral:$$ \Phi_\lambda := \oint \ldots \oint \prod_{1 \le j < k \le n} (z_j^{-1} - z_k^{-1}) \prod_{j=1}^n \prod_{k=1}^n (1 - z_j x_k)^{-1} \prod_{j=1}^n ...
I have a minor result which I'm sure has come up somewhere before but I can't seem to find it. Consider a confluent hypergeometric function of the form \newcommand{\ff}{{}_1F_1} \ff(b+k;b;z)\...