d'Alembert's formula

Named after the French physicist and mathematician Jean le Rond d'Alembert, who derived it in 1747.

d'Alembert's formula

1. (mathematics) The general solution to the one-dimensional wave equation ${\displaystyle u_{tt}-c^{2}u_{xx}=0,\,u(x,0)=g(x),\,u_{t}(x,0)=h(x),}$ for ${\displaystyle -\infty <x<\infty ,\,\,t>0}$.