Relations between double series and single series

Double Sequences and Double Series

This research considers two traditional important questions, which are interesting, at least to most mathematicians. The first question arises in the theory of double sequences of complex numbers, which concerns the relationship, if any, between the following three limits of a double sequence s : N×N −→ C: 1. limn,m→∞ s(n, m), 2. limn→∞(limm→∞ s(n, m)), 3. limm→∞(limn→∞ s(n, m)). In particular,...

Double shuffle relations of double zeta values and the double Eisenstein series at level N

In their seminal paper, Gangl, Kaneko and Zagier defined a double Eisenstein series and used it to study the relations between double zeta values. One of their key ideas is to study the formal double space and apply the double shuffle relations. They also proved the double shuffle relations for the double Eisenstein series. More recently, Kaneko and Tasaka extended the double Eisenstein series ...

Uniform convergence of single and double sine series and integrals

Characterization of Single and Double Beam Series Lateral Switch

Contiguous relations of hypergeometric series

The 15 Gauss contiguous relations for 2F1 hypergeometric series imply that any three 2F1 series whose corresponding parameters differ by integers are linearly related (over the field of rational functions in the parameters). We prove several properties of coefficients of these general contiguous relations, and use the results to propose effective ways to compute contiguous relations. We also di...