Rankin-Cohen Brackets and van der Pol-Type Identities for the Ramanujan's Tau Function

We use Rankin-Cohen brackets for modular forms and quasimodular forms to give a different proof of the results obtained by D. Lanphier and D. Niebur on the van der Pol type identities for the Ramanujan's tau function. As consequences we obtain convolution sums and congruence relations involving the divisor functions.