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 RECURRENCES OF THE JACOBSTHAL SEQUENCE
Dişkaya, Orhan | Menken, Hamza
In the present work, two new recurrences of the Jacobsthal sequence are defined. Some identities of these sequences which we call the Jacobsthal array is examined. Also, the generating and series functions of the Jacobsthal array are obtained.
On the Lagrange Interpolations of the Jacobsthal and Jacobsthal-Lucas Sequences
Dişkaya, Orhan
This study explores the formation of polynomials of at most degree nusing the first n+1 terms of the Jacobsthal and Jacobsthal-Lucas sequences through Lagrange interpolation. The paper provides a detailed examination of the recurrence relations and various identities associated with the Jacobsthal and Jacobsthal-Lucas Lagrange Interpolation Polynomials.
ON THE JACOBSTHAL AND JACOBSTHAL-LUCAS SUBSCRIPTS
Dişkaya, Orhan | Menken, Hamza
In the present work we consider the Jacobsthal and Jacobsthal- Lucas sequences with the Jacobsthal and Jacobsthal-Lucas subscripts sequences; that is, the numbers of the form Xn = JJn, Zn = Jjn, Yn = jjn and Tn = jJn. We obtain some identities and relations for the Jacobsthal and Jacobsthal- Lucas subscripts sequences. Also, we give recursive definitions for the sequences Xn, Zn, Yn and Tn.
On the Quadra Fibona-Pell and Hexa Fibona-Pell-Jacobsthal Sequences
Dişkaya, Orhan | Menken, Hamza
In this paper, we consider the Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas sequences. We introduce the quadra Fibona-Pell,Fibona-Jacobsthal and Pell-Jacobsthal and the hexa Fibona-Pell- Jacobsthal sequences whose compounds are the Fibonacci, Pell and Jacobsthal sequences. We derive the Binet-like formulas, the generating functions and the exponential generating functions of these sequences. Also, we obtain some binomial identities for them.