2018/08/15 by Sergei Kalmykov, Kalmykov, S. I., Dmitrii Karp +1
Mathematics · #26A51 #33D15 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1808.05105
openalex publication_date 2018/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shift of all its parameters. For a particular case of Heine's basic hypergeometric function we prove logarithmic concavity and convexity with respect to the bottom parameter. We further establish a linearization identity for the generalized Turánian formed by a particular case of Heine's basic hypergeometric function. Its q=1 case also appears to be new.