On Positivities of Certain q-Special Functions

2019/01/03 by Zhang, Ruiming
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.03368

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 and q-Gamma function Γ_q.

Related

• Some new inequalities for the q-gamma and related functions
• On Certain Positive Semidefinite Matrices of Special Functions
• Fourier transforms of positive definite kernels and the Riemann ξ-Function
• On the (p,q)-Gamma and the (p,q)-Beta functions
• A general positivity result on coefficients of certain q-series