A unified point of view on the theory of generalized Bessel functions (original) (raw)
A note on the theory ofn-variable generalized bessel functions
Il Nuovo Cimento B, 1991
In this note we introduce a further generalization of Bessel-type functions, discussing the case of a multivariables and one-index function. This kind of function can be usefully exploited in problems in which the dipole approximation does not hold and many higher harmonics are simultaneously operating. We analyse the relevant recurrence properties, the modified forms and the generating functions.
An application of the generalized Bessel function
Mathematica Bohemica, 2016
We introduce and study some new subclasses of starlike, convex and closeto-convex functions defined by the generalized Bessel operator. Inclusion relations are established and integral operator in these subclasses is discussed.
The k-Bessel function of the first kind
The authors introduce a k-version k of the Bessel function of the first kind and study some basic properties. Then they present a relationship between this function and the k-Mittag-Leffler and k-Wright functions recently introduced by autors themself.
Certain geometric properties of two variable generalized Bessel functions
Journal of Mathematics and Computer Science, 2026
In this paper, we will define the normalized form of the generalized Bessel functions in k and s, k form. Sufficient conditions will be given under this study for starlikeness and convexity of normalized forms of k-Bessel function and s, k-Bessel function. Geometrical interpretation of Generalized Bessel k and s, k function for different values of k and s will also be discussed. For better understanding of the reader, some examples will be provided regarding to our approach. The graphical behaviour of these normalized functions and a comparison of graphs with classical form will also be studied to show the accuracy of results.
The basics of Bessel functions
Maths at Bondi Beach, 2023
This paper gives an historical perspective on the genesis of Bessel functions and sets out detailed proofs for basic properties using different representations of Bessel functions.
This paper is a deep exploration of the project Bessel Functions by Martin Kreh of Pennsylvania State University. We begin with a derivation of the Bessel functions Ja(x) and Ya(x), which are two solutions to Bessel's differential equation. Next we find the generating function and use it to prove some useful standard results and recurrence relations. We use these recurrence relations to examine the behavior of the Bessel functions at some special values. Then we use contour integration to derive their integral representations, from which we can produce their asymptotic formulae. We also show an alternate method for deriving the first Bessel function using the generating function. Finally, a graph created using Python illustrates the Bessel functions of order 0, 1, 2, 3, and 4.
The simultaneous computation of Bessel functions of first and second kind
Computers & Mathematics with Applications, 1996
Based on the qualitative properties of Bessel's differential equation and its solutions, a method is proposed for the simultaneous evaluation of Bessel functions of first and second kind. Special attention is paid to the numerical properties of the method and to the errors of approximation. geywords-Bessel function evaluation, Singular ODE, ODE on infinite interval, Priifer transformation.
Some Nonstandard Treatments of Bessel Function
Salahaddin University-Erbil, 2015
Ibrahim Othman Hamad" for his constant and valuable guidance and encouragement during my research work. His attention, support and timely suggestions were useful and the most needed in the preparation of my Master's thesis. I'm also grateful to him for introducing me to the nice combine area of Nonstandard Analysis and Special functions. Also, my deep thanks due to "Prof Dr. Tahir H. Ismail" for his precise comments and best remarks. My sincere thanks and appreciation are extended to the Presidency of Salahaddin University-Erbil, especially the deanery of the College of Science departments for their facilities to carry out my research work. My thanks go to Assist. Prof. "Dr. Herish O. Abdullah" the head of Mathematics Department at the College of Science, further more I wish to thanks the staff members of the College of Science, especially the library staff of the College of Science and Mathematics together. Finally, I would like to state my heartily thanks to my dear wife "Suham", and my family especially my father and my mother as they brought me up to the stage. Also, thanks to all of those who taught me even one word that helped me in my study.
Certain New Integral Formulas Involving the Generalized Bessel Functions
Bulletin of the Korean Mathematical Society, 2014
A remarkably large number of integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas involving various Bessel functions have been presented. Very recently, Choi and Agarwal derived two generalized integral formulas associated with the Bessel function Jν (z) of the first kind, which are expressed in terms of the generalized (Wright) hypergeometric functions. In the present sequel to Choi and Agarwal's work, here, in this paper, we establish two new integral formulas involving the generalized Bessel functions, which are also expressed in terms of the generalized (Wright) hypergeometric functions. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.