# On a generalization of the Bessel function Neumann expansion

@article{Koskela2017OnAG, title={On a generalization of the Bessel function Neumann expansion}, author={Antti Koskela and Elias Jarlebring}, journal={arXiv: Numerical Analysis}, year={2017} }

The Bessel-Neumann expansion (of integer order) of a function $g:\mathbb{C}\rightarrow\mathbb{C}$ corresponds to representing $g$ as a linear combination of basis functions $\phi_0,\phi_1,\ldots$, i.e., $g(z)=\sum_{\ell = 0}^\infty w_\ell \phi_\ell(s)$, where $\phi_i(z)=J_i(z)$, $i=0,\ldots$, are the Bessel functions. In this work, we study an expansion for a more general class of basis functions. More precisely, we assume that the basis functions satisfy an infinite dimensional linear ordinary…

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