The `1/9'-problem for the $\phi$-functions

Thomas Schmelzer

The functions ${\phi }_{\ell }(z)=(e^z-s_{\ell }(z))/z^{\ell }$, with $s_{\ell }$ the Taylor polynomial of $e^z$ of degree $\ell -1$, are what exponential integrators evaluate, and they evaluate them…