A Treatise on the Theory of Bessel Functions, Volume 1

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 J₁ Journal für Math Jv+m Kapteyn Lommel London Math method Modern Analysis negative Neumann series Neumann's notation obtained Phil Phys 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