function is defined as the inverse function of
which plays an important role for solving equations containing exponentials or logarithms. Therefore this function is available in computer algebra systems like Maple (LambertW
) and Mathematica (ProductLog
). In the current paper the author considers a hierarchy of hyper-Lambert functions, and shows how these functions can be used to solve algebraically an infinite class of unsolvable transcendental equations, an infinite class of unsolvable differential equations, the equation
and Kepler’s equation.