English

On Positivities of Certain q-Special Functions

Classical Analysis and ODEs 2019-01-14 v1

Abstract

In this work we shall apply the Bochner's theorem to prove certain combinations of Euler's q-exponentials are positive definite functions. Then we apply this positivity to prove curious inequalities for the Jacobi theta function ϑ4\vartheta_{4} and q-Gamma function Γq\Gamma_{q}.

Keywords

Cite

@article{arxiv.1901.03368,
  title  = {On Positivities of Certain q-Special Functions},
  author = {Ruiming Zhang},
  journal= {arXiv preprint arXiv:1901.03368},
  year   = {2019}
}
R2 v1 2026-06-23T07:08:32.878Z