< 1 >
Power series for the Lambert W function
This development of the Lambert W function also applies to complex values of x
Taylor series
The Taylor series of W0 around 0 can be calculated with the inverse Lagrange theorem and is
The radius of convergence is −1/e, which you can determine in the ratio test. The function defined by this sequence can be extended to a holomorphic function defined for all complex numbers with a branching point along the interval (−∞, −1/e]. This holomorphic function is the main branch of the Lambert W function.
HistoryThe German-Swiss mathematician Johann Heinrich Lambert (1728 - 1777) described this power series. |