The main results are functional central limit theorems for superpositions of randomly selected partial sums in which the random variables being summed are independent and have distributions in the ...

We continue the work of Szegö and others on describing the convergence of the zeros, $\left\{ {{z_k},n} \right\}_{k = 1}^n$ of the normalized partial sum sn (nz) of ...

Convergence theorems form the backbone of probability theory and statistical inference, ensuring that sequences of random variables behave in a predictable manner as their index grows. These theorems, ...

Fourier series have long served as a cornerstone for representing periodic functions through harmonic components. In higher dimensions, these tools become indispensable for analysing complex systems, ...

I was having dinner with a visiting colleague this week when talk turned to what we were teaching this term. He mentioned the part of calculus dealing with infinite series (the bane of many students) ...