Watson G.N. Theory of Bessel Functions

Academic Press, 1978. - 343 Pages. This book is mainly about four functions denoted by r, R, S, and 2 F 0 . The first is the gamma function, Euler's extension of the factorial function 11! to nonintegral values of 11. The other three are hypergeometric functions and embrace as special cases the functions named after Bessel, Hankel, Legendre, Gauss, Kummer, Whittaker, Jacobi, Chebyshev, Gegenbauer, Laguerre, Hermite, and others. The R function u...

2001 by Chapman & Hall/CRC Green’s Functions for Ordinary Differential Equations Green’s Functions for the Wave Equation Green’s Function for the Heat Equation Green’s Function for the Helmholtz Equation The Fourier Transform The Laplace Transform Bessel Functions Relationship between Solutions of Helmholtz’s and Laplace’s Equations in Cylindrical and Spherical Coordinates

Prentice Hall, 1987. - 532 p. This text discusses elementary partial differential equations in the engineering and physical sciences. It is suited for courses whose titles include Fourier series, orthogonal functions, or boundary value problems. It may also be used in courses on Green's functions or transform methods. Simple models (heat flow, vibrating strings and membranes) are emphasized. Equations are formulated carefully from physical princi...

Sрringer, 2005. - 512 pages. This book, dedicated to Mizan Rahman, is made up of a collection of articles on various aspects of q-series and special functions. Also, it includes an article by Askey, Ismail, and Koelink on Rahman’s mathematical contributions and how they influenced the recent upsurge in the subject. Audience This book is intended for researchers and graduate students in special functions, algebraic combinatorics, quantum groups...

Publisher: Birkh?usеr, Bоston, 1988, 427 pages Authors of this book have collected the material on special functions that is most important in mathematical physics and quantum mechanics. They have not attempted to provide the most extensive collection possible of information about special functions, but have set ourselves the task of finding an exposition which, based on a unified approach, ensures the possibility of applying the theory in other...

2002. - 80 с. Представленная на английском языке работа - курс лекций Паламодова, подробно объясняющая решение уравнений математической физики из 8 частей. Contents Chapter 1: Differential equations of Mathematical Physics Differential equations of elliptic type Diffusion equations Wave equations Systems Nonlinear equations Hamilton-Jacobi theory Relativistic field theory Classification Initial and boundary value problems Inverse problems C...

American Mathematical Society, 2011. - 526 pages. Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems-rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the...

Addison-Wesley, 1966. - 357 Pages. In its discussions of mathematical entities and their elementary properties, this text employs examples from the physical sciences. Its concise treatment covers preliminary results in the integral calculus, distribution theory, Fourier series and transforms, the Laplace transform, the wave and heat conduction equations, and gamma and Bessel functions.

Springer, 2011. - 308 pages. Pseudodifferential analysis, introduced in this book in a way adapted to the needs of number theorists, relates automorphic function theory in the hyperbolic half-plane ? to automorphic distribution theory in the plane. Spectral-theoretic questions are discussed in one or the other environment: in the latter one, the problem of decomposing automorphic functions in ? according to the spectral decomposition of the mod...

Academic Press, 1975. - 267 pages. This book is designed for students who have had no previous knowledge of the theory of heat conduction nor indeed of the general theory of partial differential equations. On the other hand, a degree of mathematical sophistication is assumed, in that the reader is expected to be familiar with the basic results of the theory of functions of a complex variable, Laplace transform theory, and the standard working to...