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Asymptotics for some fundamental [formula omitted]-functions

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Volume
400
Issue
1
Identifiers
DOI: 10.1016/j.jmaa.2012.10.022
Keywords
  • [Formula Omitted]-Exponential [Formula Omitted]
  • [Formula Omitted]-Gamma Function [Formula Omitted]
  • [Formula Omitted]-Shifted Factorial [Formula Omitted]
  • Gaussian Coefficients [Formula Omitted]
  • Asymptotics

Abstract

Abstract In this work we derive asymptotic formulas for the q-exponential function eq(z), q-gamma function Γq(z), and q-shifted factorial (z;q)n as q approaches 1 without using theta functions or summation formulas. These asymptotics are valid uniformly on compact subsets of the complex plane.

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