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We define a new difference equation analogue of the Bessel differential equation and investigate the properties of its solution, which we express using a 2 F 1 ₂F₁ hypergeometric function. We find analogous formulas for Bessel function recurrence relations, a summation transformation which is identical to the Laplace transform of classical Bessel functions, and oscillation.
Böhner et al. (2016) studied this question.