Constructing the Neumann series -- an example
The Neumann series for the integral equation \(\theta(\xi)=\theta_ 0+\nu\int^ \ell_ 0\theta(\varepsilon)K(\xi,\varepsilon)d\varepsilon\), in which \(K(\xi,\varepsilon)=\{\xi\text{ for } \xi<\varepsilon;\;\varepsilon\text{ for } \xi>\varepsilon\}\), leads to the solution \(\theta(\xi)=\theta_ 0\times\sec\sqrt \nu\ell\cos\sqrt \nu(\ell-\xi)\), for every \(\nu\) distinct of an eigenvalue \(\nu_ j=[(2j- 1)\pi/(2\ell)]^ 2\), \(j=1,2,\ldots\).
scientific article; zbMATH DE number 26733