We study the -analogue of Euler-Maclaurin formula and by introducing a new -operator we drive to this form. Moreover, approximation properties of -Bernoulli polynomials are discussed. We estimate the suitable functions as a combination of truncated series of -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.
M. Momenzadeh. I. Y. Kakangi. "Approximation Properties of -Bernoulli Polynomials." Abstr. Appl. Anal. 2017 1 - 6, 2017. https://doi.org/10.1155/2017/9828065