On the numerical evaluation of an oscillating infinite series
The series has the form \(\Sigma m\{m(m^ 2+u^ 2)^{-1}-1\}J_ 0(am)J_ 0(bm),\) where u, a, b are constants. This is not suitable for direct numerical evaluation because of the oscillation of the Bessel functions. It is transformed by contour integration and the ingenious use of Bessel function identities into a tractable form. Some results for special cases are presented in diagrams.
scientific article; zbMATH DE number 4121268