11 papers
On Series Involving Cubed Catalan Numbers
Kunle Adegoke
Using generalized binomial coefficient identities and some results of John Dougall, we derive some families of series involving the cubes of Catalan numbers. We also establish a fa…
On Touchard's Identity: Generalizations and Related Results
Kunle Adegoke
Starting with a known polynomial identity, we derive two generalizations of Touchard's identity concerning Catalan numbers; one obtained using the Beta function and the other via a…
Applications of an identity of Batır
Kunle Adegoke, Robert Frontczak
Based on an interesting identity of Batır we derive new identities for double sums involving famous number sequences. We also prove some double sum identities for binomial transfo…
Binomial Transforms and the Binomial Convolution of Sequences
Kunle Adegoke
Given any two sequences of complex numbers, we establish simple relations between their binomial convolution and the binomial convolution of their individual binomial transforms. W…
Double sums associated with binomial transforms
Kunle Adegoke, Robert Frontczak, Karol Gryszka
In this paper, we continue our investigation of double sums where the inner sum is binomial but incomplete. We prove many new results for these types of double sums associated with…
Double sums involving binomial coefficients and special numbers
Kunle Adegoke, Robert Frontczak, Karol Gryszka
In this paper, we find an elementary approach for double sums where the inner sum is binomial but incomplete. We apply our core identity and its relatives to double sums involving…