In this paper we analyze relations among several types of convergences of bounded sequences, in particulars among statistical convergence, ${ℐ}_u$-convergence, $\varphi$-convergence, almost convergence, strong $p$-Cesàro convergence and uniformly strong $p$-Cesàro convergence.

The paper is concerned with the resurgence of the Kontsevich-Zagier series$$f\left(q\right)=\sum _{n=0}^{\infty }(1-q)\cdots (1-q^n)$$We give an explicit formula for the Borel transform of the power series when $q=e^{1/x}$ from which its analytic continuation, its singularities (all on the positive real axis) and the local monodromy can be manifestly determined. We also give two formulas (one involving the Dedekind eta function, and another involving the complex error function) for the right, left and median summation of the Borel transform. We also prove that the...