55 citations · 212 across the 44 of their papers we have counts for
26 papers · 1 filter
On a series of Ramanujan, dilogarithm values, and solitons
Khristo Boyadzhiev, Steven Manns
We discuss several topics related to polylogarithms with focus on dilogarithms. The topics are: a generating function with harmonic numbers coming from Ramanujan, extending the dil…
Identities for squared central binomial coefficients
Khristo N. Boyadzhiev
We prove four identities for the squared central binomial coefficients. The first three of them reflect certain transformation properties of the complete elliptic integrals of the…
Evaluation of binomial series with harmonic numbers
Khristo N. Boyadzhiev
We define a special function related to the digamma function and use it to evaluate in closed form various series involving binomial coefficients and harmonic numbers.
Dirichlet series and series with Stirling numbers
Khristo N. Boyadzhiev
This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers o…
Sums of powers and special polynomials
Khristo N. Boyadzhiev
In this paper, we discuss sums of powers of the positive integers and compute both the exponential and ordinary generating functions for these sums. We express these generating fun…
Stirling numbers and inverse factorial series
Khristo N. Boyadzhiev
We study inverse factorial series and their relation to Stirling numbers of the first kind. We prove a special representation of the polylogarithm function in terms of series with…