Characterizing <i>q</i>-Bessel Functions of the First Kind with Their New Summation and Integral Representations

Abstract

As a powerful tool for models of quantum computing, q-calculus has drawn the attention of many researchers in the discipline of special functions. In this paper, we present new properties and characterize q-Bessel functions of the first kind using some identities of q-calculus. The results presented in this article help us to obtain new expression results related to q-special functions. New summation and integral representations for q-Bessel functions of the first kind are also established. A few examples are also provided to demonstrate the effectiveness of the proposed strategy.

Keywords

• quantum calculus
• Bessel function
• q-shift factorial
• q-Bessel function
• q-hypergeometric function