A Treatise on the Theory of Bessel Functions

absolutely convergent analysis analytic analytic continuation analytic function Archiv der Math asymptotic expansions Bessel coefficients Bessel functions Bessel's equation Camb contour integral cos² cosh cylinder functions deduce defined differential equation equal Euler expression follows Fourier series Fourier-Bessel Fourier-Bessel series Functions of order Gegenbauer generalised given Hankel's Hence integer integrand interval investigation Journal für Math Lommel London Math memoir method negative Neumann Neumann series notation obtained Phil Phys places of decimals Poisson's integral polynomial positive integer positive number positive zeros Proc proof prove real axis recurrence formulae replace result Riemann-Lebesgue lemma Royal Soc Schafheitlin Schlömilch shew shewn sin² sinh solution Table theorem theory uniformly valid values variables write г µ