Approximation Properties of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>-Bernoulli Polynomials
Approximation Properties of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>-Bernoulli Polynomials
We study the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>-analogue of Euler-Maclaurin formula and by introducing a new <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>-operator we drive to this form. Moreover, approximation properties of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>-Bernoulli polynomials are discussed. We estimate the suitable functions as a combination of truncated series of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>-Bernoulli polynomials and the …