Mathematics

Problem

For the Lagrangian

\mathcal{L}

given by

\mathcal{L} = \frac{1}{2} \partial^\mu \phi \partial_\mu \phi - \frac{1}{2} m^2 \phi^2 - \sum_{n=1}^{\infty} \lambda_n \phi^{2n+2}, \quad (7.20)

show that the equation of motion is given by

(\partial^2 + m^2)\phi + \sum_{n=1}^{\infty} \lambda_n (2n+2) \phi^{2n+1} = 0. \quad (7.21)