Convergence Aspects for q‐Appell Functions and q‐Lauricella Functions with Applications to the Ward q‐Addition Available to Purchase

We first outline the foundations of the q‐umbral calculus, which consists of an infinite alphabet A of letters or umbrae, with two dual q‐additions, the Nalli‐Ward‐Alsalam (NWA) q‐addition and the Jackson‐Hahn‐Cigler (JHC) q‐addition. By using a certain q‐Stirling approximation, we show that the NWA decides the convergence region for 50% of the q‐Appell‐ and q‐Lauricella functions. This assumption is verified by numerical examples. In the process we investigate numerical aspects, including a local maximum, of the NWA q‐addition of two and three letters.