${\displaystyle \underset{\text{V}}{\iiint }\left(\mathrm{grad}{f}_1\cdot grad{f}_2+f_1\Delta f_2\right)}dV={\displaystyle \underset{\text{S}}{∯}{f}_1}grad{f}_2\cdot e_{\text{n}}dA$

where dV is the volume element, e_ndA is the vector surface element and Δ is the Laplacian operator

Note 1 to entry: In English the first Green formula is sometimes called “first Green theorem” or “first Green identity”.