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In this volume we study the generalized Bessel functions of the
first kind by using a number of classical and new findings in
complex and classical analysis. Our aim is to present interesting
geometric properties and functional inequalities for these
generalized Bessel functions. Moreover, we extend many known
inequalities involving circular and hyperbolic functions to Bessel
and modified Bessel functions.
This book is devoted to the study of certain integral
representations for Neumann, Kapteyn, Schloemilch, Dini and Fourier
series of Bessel and other special functions, such as Struve and
von Lommel functions. The aim is also to find the coefficients of
the Neumann and Kapteyn series, as well as closed-form expressions
and summation formulas for the series of Bessel functions
considered. Some integral representations are deduced using
techniques from the theory of differential equations. The text is
aimed at a mathematical audience, including graduate students and
those in the scientific community who are interested in a new
perspective on Fourier-Bessel series, and their manifold and
polyvalent applications, mainly in general classical analysis,
applied mathematics and mathematical physics.
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