New results on the q-generalized Bernoulli polynomials of level m

This paper aims to show new algebraic properties from the q -generalized Bernoulli polynomials <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:msubsup> <m:mrow> <m:mi>B</m:mi> </m:mrow> <m:mi>n</m:mi> <m:mrow> <m:mo stretchy="false">[</m:mo> <m:mi>m</m:mi> <m:mo>-</m:mo> <m:mn>1</m:mn> <m:mo stretchy="false">]</m:mo> </m:mrow> </m:msubsup> <m:mo stretchy="false">(</m:mo> <m:mi>x</m:mi> <m:mo>;</m:mo> <m:mi>q</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> B_n[m - 1](x;q) of level m , as well as some others identities which connect this polynomial class with the q -generalized Bernoulli polynomials of level m , as well as the q -gamma function, and the q -Stirling numbers of the second kind and the q -Bernstein polynomials.