Baricz, Árpád.
Series of Bessel and Kummer-Type Functions [electronic resource] / by Árpád Baricz, Dragana Jankov Maširević, Tibor K. Pogány. - 1st ed. 2017. - XIX, 201 p. online resource. - Lecture Notes in Mathematics, 2207 0075-8434 ; . - Lecture Notes in Mathematics, 2207 .
1. Introduction and Preliminaries -- 2. Neumann Series -- 3. Kapteyn Series -- 4. Schlomilch Series -- 5. Miscellanea.
This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlömilch, 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.
9783319743509
10.1007/978-3-319-74350-9 doi
Special functions.
Sequences (Mathematics).
Functions of real variables.
Functions of complex variables.
Differential equations.
Astronomy.
Astrophysics.
Special Functions.
Sequences, Series, Summability.
Real Functions.
Functions of a Complex Variable.
Ordinary Differential Equations.
Astronomy, Astrophysics and Cosmology.
QA351
515.5
Series of Bessel and Kummer-Type Functions [electronic resource] / by Árpád Baricz, Dragana Jankov Maširević, Tibor K. Pogány. - 1st ed. 2017. - XIX, 201 p. online resource. - Lecture Notes in Mathematics, 2207 0075-8434 ; . - Lecture Notes in Mathematics, 2207 .
1. Introduction and Preliminaries -- 2. Neumann Series -- 3. Kapteyn Series -- 4. Schlomilch Series -- 5. Miscellanea.
This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlömilch, 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.
9783319743509
10.1007/978-3-319-74350-9 doi
Special functions.
Sequences (Mathematics).
Functions of real variables.
Functions of complex variables.
Differential equations.
Astronomy.
Astrophysics.
Special Functions.
Sequences, Series, Summability.
Real Functions.
Functions of a Complex Variable.
Ordinary Differential Equations.
Astronomy, Astrophysics and Cosmology.
QA351
515.5