5 papers
Harmonic Catalan Number Series via Half-Integer Binomial Coefficients
Kunle Adegoke, Robert Frontczak, Taras Goy
We develop a method for evaluating finite and infinite series involving Catalan numbers by specializing alternating binomial identities at half-integer parameters. The key ingredie…
Abel-Type Transformations and Telescoping Structures in Reciprocal Series of Second-Order Linear Recurrences
Kunle Adegoke, Robert Frontczak, Taras Goy
We develop a unified method for transforming and evaluating infinite series involving products of terms of second-order linear recurrences in the denominator. The approach is based…
Fibonacci-harmonic sums
Kunle Adegoke, Segun Olofin Akerele, Robert Frontczak
We offer several new summation identities involving harmonic numbers, odd harmonic numbers, and Fibonacci numbers. Our results are derived using three different approaches: partial…
Fibonacci sums modulo 5
Kunle Adegoke, Robert Frontczak, Taras Goy
We develop closed form expressions for various finite binomial Fibonacci and Lucas sums depending on the modulo 5 nature of the upper summation limit. Our expressions are inferred…
New binomial Fibonacci sums
Kunle Adegoke, Robert Frontczak, Taras Goy
We present some new linear, quadratic, cubic and quartic binomial Fibonacci, Lucas and Fibonacci--Lucas summation identities.