1996/08/31 by Charles A. Nelson, Michael G. Gartley, Michael G Gartley
Computer Science · Mathematics · #Advanced Mathematical Identities #Mathematical functions and polynomials #Polynomial and algebraic computation #math.QA #q-alg
paper · pdf · doi:10.1088/0305-4470/29/24/031
This is the final version to appear in J.Phys.A: Math. & General. Some explict formulas added, and to update the references
arxiv created 1996/09/27 · openalex publication_date 1996/12/21 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
There is a simple, multi-sheet Riemann surface associated with 's inverse function for . A principal sheet for can be defined. However, the topology of the Riemann surface for changes each time q increases above the collision point of a pair of the turning points of . There is also a power series representation for . An infinite-product representation for is used to obtain the ordinary natural logarithm and the values of the sum rules for the zeros of . For , where . The values of the sum rules for the q-trigonometric functions, and , are q-deformations of the usual Bernoulli numbers.