Rusev P. An invitation to Bessel functions / Bulg. Acad. of Sciences, Inst. of mathematics a. informatics. - Sofia: Prof. Marin Drinov Publishing House of Bulgarian Academy of Sciences, 2016. - 181 p. - Bibliogr.: p.181. - ISBN 978-954-322-871-3 Шифр: (И/В16-R95) 02  Место хранения:   02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents

Preface ......................................................... 7 Chapter 1. Introduction to the theory of Bessel functions ...... 15 1.1 Bessel differential equation .............................. 15 1.2 Bessel functions of first kind ............................ 18 1.3 Bessel functions of second kind ........................... 20 1.4 Bessel functions in complex domain ........................ 25 1.5 Modified Bessel functions ................................. 30 1.6 Spherical Bessel functions ................................ 32 1.7 Integral representations of Bessel functions .............. 35 1.8 Asymptotic formulas for Bessel functions .................. 39 1.9 Zeros of Bessel functions ................................. 54 1.10 Functions related to Bessel functions .................... 63 1.11 Integrals involving Bessel functions ..................... 69 Comments and references to Chapter 1 ........................... 74 Chapter 2. Bessel's series and integral representations ........ 81 2.1 Series of Fourier-Bessel and Dini ......................... 81 2.2 Series of Schlomilch ...................................... 97 2.3 Series of Neumann ........................................ 104 2.4 Integral of Hankel ....................................... 110 2.5 Integral of Hardy ........................................ 115 2.6 Integral of Meijer ....................................... 122 Comments and references to Chapter 2 .......................... 129 Chapter 3. Bessel's integral transforms ....................... 135 3.1 Mellin transform and reciprocal kernels of Fourier type .. 135 3.2 H-transforms ............................................. 141 3.3 Y-transforms ............................................. 145 3.4 K-transforms ............................................. 149 Comments and references to Chapter 3 .......................... 152 Addendum. Analytic solutions of linear second order differential equations ................................... 153 Appendix. The Euler gamma-function ............................ 163 Exercises ..................................................... 175 Bibliography .................................................. 181