Approximation Properties of q-Bernoulli Polynomials

الملخص EN

We study the q-analogue of Euler-Maclaurin formula and by introducing a new q-operator we drive to this form.

Moreover, approximation properties of q-Bernoulli polynomials are discussed.

We estimate the suitable functions as a combination of truncated series of q-Bernoulli polynomials and the error is calculated.

This paper can be helpful in two different branches: first we solve the differential equations by estimating functions and second we may apply these techniques for operator theory.