## Taylor polynomials for nabla dynamic equations on time scales.(English)Zbl 1026.34011

Summary: We are concerned with the representation of polynomials for nabla dynamic equations on time scales. Once established, these polynomials are used to derive Taylor’s formula for dynamic functions. Several examples are given for special time scales such as $$\mathbb{Z},\mathbb{R}$$, and $$\overline\mathbb{Z}$$ for $$q>1$$. These polynomials are related to those given for delta dynamic equations.

### MSC:

 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 39A10 Additive difference equations

### Keywords:

Taylor polynomials; nabla dynamic equations; time scales