Sir William Rowan Hamilton's Fluctuating Functions

A contribution to the theory of the Fourier integral formula

“…We deal in our presentation with these conditions introducing the concept of a Dirichlet-point of f(x) and a Dirichlet-value DI(x ) of f(x) in such a point, which could be characterized as a point of convergence of the corresponding Fourier-series and the value of this series in such a point. 4. As to the convergence conditions qualifying the infinitary behaviour of f(x), usually two conditions are considered:…”