A Note on <i>q</i>-analogue of Degenerate Catalan Numbers Associated with <i>p</i>-adic Integral on <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula>

Abstract

In this paper, we introduce q-analogues of degenerate Catalan numbers and polynomials with the help of a fermionic p-adic q-integrals on Zp and establish some new connections with the degenerate Stirling numbers of the first and second kinds. Furthermore, we also find a few new identities and results of this type of polynomials and numbers.

Keywords

• <i>q</i>-Catalan numbers
• <i>q</i>-analogue of degenerate Catalan polynomials and numbers
• Stirling numbers