Some identities involving q-poly-tangent numbers and polynomials and distribution of their zeros

Abstract

Abstract In this paper we introduce the q-poly-tangent polynomials and numbers. We also give some properties, explicit formulas, several identities, a connection with poly-tangent numbers and polynomials, and some integral formulas. Finally, we investigate the zeros of the q-poly-tangent polynomials by using a computer.

Keywords

• tangent numbers and polynomials
• q-poly-tangent numbers and polynomials
• Cauchy numbers
• Stirling numbers
• Frobenius-Euler polynomials
• q-poly-Euler polynomials