# On the quantum differentiation of smooth real-valued functions

Author

Kolosov Petro

License

Creative Commons CC BY 4.0

Abstract

Calculating the value of C^{k ∈ {1, ∞}} class of smoothness real-valued function's derivative in point of **R**^{+} in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial theorem and q-difference operator. (P,q)-power difference introduced in section 5. Additionally, by means of Newton's interpolation formula, the discrete analog of Taylor series, interpolation using q-difference and p,q-power difference is shown.