Integration Sequences of Jacobsthal and Jacobsthal-Lucas Polynomials

Incomplete generalized Vieta–Pell and Vieta–Pell–Lucas polynomials

“…Finally, there are still further bridges to be built among the properties of these inter-related sequences of numbers and their associated polynomials [4,18].…”

“…These number sequences and their generalizations have found application in many fields (see, e.g., [2,5,6,7,8,14]). Many researchers have presented many features by defining the polynomials of these generalizations [4,9,10,18]. There is still scope for generalizations of the dimensions of the associated continued fraction algorithms [17].…”

On hyperbolic k-Jacobsthal and k-Jacobsthal–Lucas octonions

“…Many generalizations of number sequences were then described and studied [4,5,12,15,19]. One of these generalizations is the Jacobsthal numbers [7,8,14,15,17,19]. The Jacobsthal numbers 𝐽 𝑛 are defined by the relation 𝐽 𝑛+2 = 𝐽 𝑛+1 + 2𝐽 𝑛 , 𝑛 ≥ 0 with 𝐽 0 = 0 and 𝐽 1 = 1.…”

On the Pell-Einstein series of power m

“…Since number sequences and especially Fibonacci sequences are observed in nature, they find application in many fields of science [6,10,14,15]. In fact, many generalizations of Fibonacci sequences have been made and the relationships between them have been studied for many years [5,7,13,16]. One of these generalizations is Pell numbers.…”