Bessel Functions and Their Applications
Bessel functions are associated with a wide range of problems in important areas of mathematical physics. Bessel function theory is applied to problems of acoustics, radio physics, hydrodynamics, and atomic and nuclear physics. Bessel Functions and Their Applications consists of two parts. In Part One, the author presents a clear and rigorous introduction to the theory of Bessel functions. Part Two is devoted to the application of Bessel functions to physical problems, particularly in the mechanics of solids and heat transfer. This volume was designed for engineers and researchers interested in the applications of the theory, and as such, it provides an indispensable source of reference.
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addition formulae applied assume asymptotic expansions basic solution bending Bessel functions Bessel integral boundary conditions calculation circular plate circumference coefficients compensating loadings compensating solution complex argument concentrated force consider the problem constant contains contour coordinates cross-section deflection denote differential equation domain elastic foundation equal to zero expression following form Fredholm equation free oscillations gamma functions given Hankel function Hankel transform Helmholtz equation hence immediately obtain implies improper integrals influence function inhomogeneous Bessel equation integral equations integral representations integrand introduce Jv(z kernel Let us give linear Lommel functions membrane method non-integer obtain the following Obviously partial cylindrical functions particular solution plane Poisson integral power function power series recurrence relations replace represented result right-hand side roots shown in Fig solution of equation solved Sonin integral Struve function term theory of Bessel transcendental equation transform transversal force values vanish variable Wronskian
Page ii - ANALYTICAL METHODS AND SPECIAL FUNCTIONS An International Series of Monographs in Mathematics EDITOR IN CHIEF: AP Prudnikov (Russia) ASSOCIATE EDITORS: CF Dunkl (USA), H.-J. Glaeske (Germany) and M. Saigo (Japan...
Page viii - Bessel functions considered in the second part of the book. The book consists of two parts. The first part...
Page viii - Neumann addition theorems and the foundation of the theory of products of Bessel functions are considered. Questions concerning differential equations which can be reduced to the Bessel equation and the inhomogeneous Bessel equations are considered in detail.
Page ix - Winkler-type foundation are considered, a§ well as problems which can be reduced to the use of the method of compensating loadings. The method of initial parameters is considered in detail in the context of the problem of the axially symmetrical deformation of a circular conic shell.
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