A Second Type Of Higher Order Generalised Geometric Polynomials and Higher Order Generalised Euler Polynomials

In this study we introduce a second type of higher order generalised geometric polynomials. This we achieve by examining the generalised stirling numbers $S(n; k;α;β;γ)$ [Hsu & Shiue,1998] for some negative arguments. We study their number theoretic properties, asymptotic properties, and study their combinatorial properties using the notion of barred preferential arrangements. We also proposed a generalisation of the classical Euler polynomials and show how these Euler polynomials are related to the second type of higher order generalised geometric polynomials.

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