Ahmet YantirBurcu Silindir YantirZehra TuncerYantir, Burcu SilindirTuncer, ZehraYantir, Ahmet2025-10-0620221300-00981303-614910.3906/tar-2201-142http://dx.doi.org/10.3906/tar-2201-142https://gcris.yasar.edu.tr/handle/123456789/6948https://doi.org/10.3906/tar-2201-142This article is devoted to present nabla (q h)-analogues of Bessel equation and Bessel function. In order to construct series solution of nabla (q h)-Bessel equation we present nabla (q h)-analysis regarding nabla generalized quantum binomial nabla (q h)-analogues of Taylor's formula Gauss's binomial formula Taylor series analytic functions analytic exponential function with its fundamental properties analytic trigonometric and hyperbolic functions. We emphasize that nabla (q h)-Bessel equation recovers classical h- and q-discrete Bessel equations. In addition we establish nabla (q h)-Bessel function which is expressed in terms of an absolutely convergent series in nabla generalized quantum binomials and intimately demonstrate its reductions. Finally we develop modified nabla (q h)-Bessel equation modified nabla (q h)-Bessel function and its relation with nabla (q h)-Bessel function.Englishinfo:eu-repo/semantics/closedAccessNabla generalized quantum binomial, nabla (q, h)-Taylor series, h)-analytic functions, (q, h)-Bessel equation, h)-Bessel functionNabla (qH)-Bessel EquationH)-Taylor Series(qH)-Bessel FunctionNabla Generalized Quantum BinomialH)-Analytic FunctionsArticle