The Umbral operator and the integration
involving generalized Bessel-type functions

Nisar, Kottakkaran Sooppy; Mondal, Saiful R.; Agarwal, Praveen; Al‐Dhaifallah, Mujahed

doi:10.1515/math-2015-0041

Cited by 3 publications

(3 citation statements)

References 15 publications

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“…In the previous sections, we have developed a formalism capable of providing a unified point of view to apparently different functions; analogous ideas have also recently appeared in the literature [13], and the possibilities offered by the technique may be considered promising, if properly developed. To corroborate the previous statement, we recall that, aside from yielding a common environment for the Bessel congeries and their associates, the method allows for the derivation of previously unknown sum rules of lacunary Laguerre polynomials [14].…”

Section: Final Commentsmentioning

confidence: 99%

From Circular to Bessel Functions: A Transition through the Umbral Method

Dattoli¹,

Palma²,

Licciardi

et al. 2017

Fractal Fract

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A common environment in which to place Bessel and circular functions is envisaged. We show, by the use of operational methods, that the Gaussian provides the umbral image of these functions. We emphasize the role of the spherical Bessel functions and a family of associated auxiliary polynomials, as transition elements between these families of functions. The consequences of this point of view and the relevant impact on the study of the properties of special functions is carefully discussed.

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Section: Final Commentsmentioning

confidence: 99%

From Circular to Bessel Functions: A Transition through the Umbral Method

Dattoli¹,

Palma²,

Licciardi

et al. 2017

Fractal Fract

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“…A solution of the homogeneous modified Bessel equation gives the modified Bessel function of order p Because of its importance, the Bessel function and other special functions are of continued interest to the wider scientific community. The Bessel function and its variations have gone through several generalizations, see, for example, [ 1 – 6 ]. These generalized functions have also been framed as complex-valued analytic functions in the unit disk.…”

Section: Introductionmentioning

confidence: 99%

Inequalities on an extended Bessel function

2018

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This paper studies an extended Bessel function of the form Representation formulations for are derived in terms of the parameters a, b, and p. An important consequence is the derivation of an -order differential equation satisfied by the function . Interesting functional inequalities are established, particularly for the case , and .Monotonicity properties of are also studied for non-positive c. Log-concavity and log-convexity properties in terms of the parameters d and p are respectively investigated for the closely related function which leads to direct and reverse Turán-type inequalities.

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“…Also, one is asked to look at more recent papers on umbral calculus (Nisar et al. 2015 ; Srivastava et al. 2014 ).…”

Section: Introductionmentioning

confidence: 99%

Korobov polynomials of the third kind and of the fourth kind

Kim

Ким

2015

SpringerPlus

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The first degenerate version of the Bernoulli polynomials of the second kind appeared in the paper by Korobov (Math Notes 2:77–19, 1996; Proceedings of the IV international conference modern problems of number theory and its applications, pp 40–49, 2001). In this paper, we study two degenerate versions of the Bernoulli polynomials of the second kind which will be called Korobov polynomials of third kind and of the fourth kind. Some properties, identities, recurrence relations and connections with other polynomials are investigated by using umbral calculus.

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The Umbral operator and the integration involving generalized Bessel-type functions

Cited by 3 publications

References 15 publications

From Circular to Bessel Functions: A Transition through the Umbral Method

From Circular to Bessel Functions: A Transition through the Umbral Method

Inequalities on an extended Bessel function

Korobov polynomials of the third kind and of the fourth kind

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