Hahn–Exton q-Bessel function

The Hahn-Exton \( q \)-Bessel function is a special function that generalizes the classical Bessel functions in the context of \( q \)-calculus, which is a mathematical framework that extends traditional calculus to include \( q \)-analogues of various concepts. The \( q \)-Bessel functions arise in various areas of mathematics and theoretical physics, including combinatorics, quantum mechanics, and the theory of orthogonal polynomials.