ARCTANGENT IDENTITIES INVOLVING THE JACOBSTHAL AND JACOBSTHAL-LUCAS NUMBERS
Dişkaya, Orhan
This study presents novel arctangent identities that establish connections between the Jacobsthal and Jacobsthal-Lucas numbers. These findings contribute to the understanding of the interplay between trigonometric functions and number theory, particularly in relation to well-known mathematical sequences and constants.
On the Pseudo-Fibonacci and Pseudo-Lucas Quaternions
Dişkaya, Orhan | Menken, Hamza
There are a lot of quaternion numbers that are related to theFibonacci and Lucas numbers or their generalizations have been described and extensively explored. The coefficients of these quaternions have been chosen from terms of Fibonacci and Lucas numbers. In this study, we define two new quaternions that are pseudo-Fibonacci and pseudo-Lucas quaternions. Then, we give their Binet-like formulas, generating functions, certain binomial sums and Honsberg-like, d’Ocagne-like, Catalan-like and Cassini-like identities.