arXiv subjects

Jeffrey L. Meyer

Publications and source records attributed to Jeffrey L. Meyer.

2 recordsLinked to original sources

arXiv2026

Sums of Reciprocals of Generalized Triangular Numbers

We compute the sum and the alternating sum of the reciprocals of triangular numbers using two standard methods from calculus: a telescoping series approach and a power series approach. We then extend these results to generalized (higher-order) triangular numbers and derive closed-form expressions for both the non-alternating and alternating series of all orders.

math.NT↗

arXiv2026

An Arithmetic Sum Associated with the Classical Theta Function

The sum $S(h,k):=\sum_{j=1}^{k-1}(-1)^{j+1+[hj/k]}$ appears in the modular transformation formulae of the classical theta function $\vartheta_3(z)$. The double sum $S(k) := \sum_{h=1}^{k-1}S(h,k)$ has a remarkable distribution of values. Although properties for $S(k)$ and a related sum can be established, several interesting conjectures are open.

math.NT↗