Homogeneous Linear Calculus of Order 1 and a $λ$-Taylor Formula

In this paper, a new calculus on sequences is defined. Also, the $λ$-derivative and the $λ$-integration are investigated. The fundamental theorem of $λ$-calculus is included. A suitable function basis for the $λ$-derivative and the $λ$-integral is provided, and various properties of this basis are given. A $λ$-Taylor formula for functions is given.