Whittaker function

Summary

The Whittaker functions $M_{\kappa, \mu}(z)$ and $W_{\kappa, \mu}(z)$ are solutions of Whittaker's equation $w'' + \left( -\frac14 + \frac{\kappa}{z} + \frac{\frac14 - \mu^2}{z^2} \right) w = 0$. They are the confluent hypergeometric functions rewritten so that the equation has no first derivative term. This normal form is convenient in physics and in asymptotic analysis, and it makes the symmetry $\mu \mapsto -\mu$ visible.