On the Generalization of an Infinitesimal Point Transformation of Partial Differential Equations (PDEs)

symmetry analysis which is associated with Sophus Lie is one of the approaches of solution of an evolution partial differential equation. This paper extends the generator for the n-th 
prolongation of the generator of an n-th–order ordinary differential equation to a general formula for the n-th prolongation of a generator, , with k-independent and p-dependent 
variables of an n-th-order partial differential equation. With this formula, the cumbersomeness in the initial extraction of determining equations from the process of obtaining a solution is reduced. An example with a heat equation is provided to show how straightforward the formula can be in finding Lie point symmetries of partial differential equations.