8 papers
Revisiting an infinitely nested radical
Aung Phone Maw
We revisit an infinitely nested radical by Ramanujan. Utilizing the full strength of his method, we shall arrive at some new infinitely nested radicals.
On a double series
Aung Phone Maw
We shall investigate and arrive at a certain functional property of the double series \[ \sum\limits_{n,r\geq 1}\frac{1}{\sqrt{x^2n^2+r^2+w^2}\left( e^{2 πy\sqrt{x^2n^2+r^2+w^2}}-1…
Analytic expressions pertaining to certain arithmetical functions
Aung Phone Maw
We demonstrate the general outlines of a method for obtaining analytic expressions for certain types of general arithmetical sums. In particular, analytical expressions for a gener…
On certain -multiple sums
Aung Phone Maw
We present outlines of a general method to reach certain kinds of -multiple sum identities. Throughout our exposition, we shall give generalizations to the results given by Dilc…
Certain products of sums of Lambert series
Aung Phone Maw
Using elementary means, we prove an identity giving the infinite product form of a sum of Lambert series originally stated by Venkatachaliengar, then rediscovered by Andrews, Lewis…
Generalization of some of Ramanujan's formulae
Aung Phone Maw
We shall make use of the method of partial fractions to generalize some of Ramanujan's infinite series identities, including Ramanujan's famous formula for , and we shall…
On q-series identities with multiple sums related to divisor functions
Aung Phone Maw
We provide an exposition of q-identities with multiple sums related to divisor functions given by Dilcher, Prodinger, Fu and Lascoux, Zeng, Guo and Zhang. Meanwhile, for each of th…
Recursive Harmonic Numbers and Binomial Coefficients
Aung Phone Maw, Aung Kyaw
We define recursive harmonic numbers as a generalization of harmonic numbers. The table of recursive harmonic numbers, which is like Pascal's triangle, is constructed. A formula fo…