A Treatise on the Theory of Bessel FunctionsThe late Professor G.N. Watson wrote his monumental treatise on the theory of Bessel functions in 1922 with two objects in view. The first was the development of applications of the fundamental processes of the theory of complex variables, and the second was compiling a collection of results of value for mathematicians and physicists who encounter Bessel functions in the course of their researches. The completeness of the theoretical account, combined with the wide scope of the collection of practical examples have resulted in a book that will be indispensable for pure mathematicians, applied mathematicians, and physicists. |
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absolutely convergent analytic analytic continuation analytic function asymptotic expansions Bessel coefficients Bessel functions Bessel's equation Bessel'schen Functionen Leipzig Camb contour integral cos² cosh cylinder functions deduce defined differential equation eizt expression F₁ follows Fourier-Bessel Fourier-Bessel series Functions of order Gegenbauer generalised given Hankel's Hence inequalities integer integrand interval investigation Journal für Math Kapteyn Lommel London Math method Modern Analysis negative Neumann series Neumann's notation obtained Phil Phys Poisson's integral polynomial positive integer positive number positive zeros Proc proof prove recurrence formulae replace result Schläfli Schlömilch Schlömilch series shew shewn sin² sinh Table theorem uniformly uniformly convergent valid values variables г µ
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Page 760 - Earnshaw (S.) — PARTIAL DIFFERENTIAL EQUATIONS. An Essay towards an entirely New Method of Integrating them. By S. EARNSHAW, MA, St. John's College, Cambridge. Crown 8vo. $s. The peculiarity of the system expounded in this work is, that in every...