On some geometric properties and Hardy class of <i>q</i>-Bessel functions
İbrahim Aktaş
Abstract
In this paper, we deal with some geometric properties including starlikeness and convexity of order <i>α</i> of Jackson's second and third <i>q</i>-Bessel functions which are natural extensions of classical Bessel function <i>J</i><sub><i>ν</i></sub>. In additon, we determine some conditions on the parameters such that Jackson's second and third <i>q</i>-Bessel functions belong to the Hardy space and to the class of bounded analytic functions.
Topics & Concepts
Bessel functionStruve functionMathematicsConvexityHardy spaceBessel polynomialsBounded functionBessel processSpace (punctuation)Class (philosophy)Pure mathematicsFunction (biology)Mathematical analysisOrthogonal polynomialsMacdonald polynomialsComputer scienceDifference polynomialsArtificial intelligenceClassical orthogonal polynomialsGegenbauer polynomialsLinguisticsEconomicsEvolutionary biologyFinancial economicsPhilosophyBiologyAnalytic and geometric function theoryMathematical functions and polynomialsHolomorphic and Operator Theory