Ahmet YantirBurcu Sİlİndİr YantirZehra Tuncer2025-10-06202213036149, 130000981300-009810.55730/1300-0098.3334https://www.scopus.com/inward/record.uri?eid=2-s2.0-85143798381&doi=10.55730%2F1300-0098.3334&partnerID=40&md5=b1e8cc7703e384cf1abd2e6356a8ed23https://gcris.yasar.edu.tr/handle/123456789/8776This 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. © 2022 Elsevier B.V. All rights reserved.EnglishH) -analytic Functions, H) -bessel Equation, H) -bessel Function, H) -taylor Series, Nabla (q, Nabla (q, Nabla (q, Nabla (q, Nabla Generalized Quantum BinomialArticle