A Note on theq-Euler Numbers and Polynomials with Weak Weightα

[摘要] We construct a new type ofq-Euler numbers and polynomials with weak weightα:En,q(α),En,q(α)(x), respectively. Some interesting results and relationships are obtained. Also, we observe the behavior of roots of theq-Euler numbersEn,q(α)and polynomialsEn,q(α)(x)with weak weightα. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots ofq-Euler polynomialsEn,q(α)with weak weightα.

[学科分类] 应用数学