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

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