Two algorithms for computing the Randles-Sevcik function from electrochemistry. (Q1431713)

The Randles-Sevcik function \(\sqrt\Pi\chi(x)\) is defined by the integral \[ \sqrt\Pi\chi(x)=\int_0^\infty t^{1/2}\text{csch}\,{\pi t}\, \sin \left (xt+\frac \pi 4\right)dt. \] Of this function the authors establish an asymptotic expansion for \(x\to\infty \) and a Taylor expansion at any \(x_0\in\mathbb R\). Both expansions are accompanied by bounds for the remainders at any order of the approximation. The usefulness of the expansions is illustrated by numerical experiments showing the approximations that can be obtained.