We define recursive harmonic numbers as a generalization of harmonic numbers. The table of recurs... more 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.
We define recursive harmonic numbers as a generalization of harmonic numbers. The table of recurs... more 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.
We will make use of the method of partial fractions to generalize some of Ramanujan's infinite se... more We will 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). It is shown here that the method of partial fractions can be used to obtain many similar identities of this kind.
Using elementary means, we prove an identity giving the infinite product form of a sum of Lambert... more 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.
We provide an exposition of q-identities with multiple sums related to divisor functions given by... more 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.
We define recursive harmonic numbers as a generalization of harmonic numbers. The table of recurs... more 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.
We define recursive harmonic numbers as a generalization of harmonic numbers. The table of recurs... more 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.
We will make use of the method of partial fractions to generalize some of Ramanujan's infinite se... more We will 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). It is shown here that the method of partial fractions can be used to obtain many similar identities of this kind.
Using elementary means, we prove an identity giving the infinite product form of a sum of Lambert... more 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.
We provide an exposition of q-identities with multiple sums related to divisor functions given by... more 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.
Uploads
Papers by Aung Phone Maw