Revisiting an infinitely nested radical
We revisit an infinitely nested radical by Ramanujan. Utilizing the full strength of his method, we shall arrive at some new infinitely nested radicals.
math.CO↗
arXiv subjects
Aung Phone Maw
Publications and source records attributed to Aung Phone Maw.
On a double series
We shall investigate and arrive at a certain functional property of the double series \[ \sum\limits_{n,r\geq 1}\frac{1}{\sqrt{x^2n^2+r^2+w^2}\left( e^{2 πy\sqrt{x^2n^2+r^2+w^2}}-1\right)}. \]
math.CO↗
On certain $q$-multiple sums
We present outlines of a general method to reach certain kinds of $q$-multiple sum identities. Throughout our exposition, we shall give generalizations to the results given by Dilcher, Prodinger, Fu and Lascoux, Zeng, and Guo and Zhang concerning $q$-series identities related to divisor functions. Our exposition shall also provide a generalization of the duality relation for finite multiple harmonic $q$-series given by Bradley. Utilizing these generalizations, we will also arrive at some new interesting classes of $q$-multiple sums.
math.CO↗
Generalization of some of Ramanujan's formulae
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 $ζ(2n+1)$, and we shall also give a generalization of the transformation formula for the Dedekind eta function. It is shown here that the method of partial fractions can be used to obtain many similar identities of this kind.
math.GM↗
Analytic expressions pertaining to certain arithmetical functions
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 general arithmetical sum whose terms are summed over either the positive integer solutions $(a,b)$ of the Diophantine equation $kb^2+da^2 = N$ or the positive integer solutions $(a,b)$ of the Diophantine equation $kb^2-da^2 = N$ are derived. As one of the consequences, we propose a possible improvement of the Robin-Lagarias criteria for the Riemann hypothesis.
math.CO↗
Certain products of sums of Lambert series
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, and Liu. Then we derive two identities expressing certain products of sums of Lambert series.
math.GM↗
On q-series identities with multiple sums related to divisor functions
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 these identities, a more powerful statement will be derived through our exposition.
math.CO↗
Recursive Harmonic Numbers and Binomial Coefficients
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 for recursive harmonic numbers containing binomial coefficients is also presented.
math.CO↗