** Authors:**
ALİ ERDOĞAN, HALİSE MELİS TEKİN AKÇİN

** Abstract: **
Let R be a coordinate ring of an affine irreducible curve represented by \frac{k[x_1,x_2,...,x_s]}{(f)} and m be a maximal ideal of R. In this article, the Betti series of \Omega_2(R_m) is studied. We proved that the Betti series of \Omega_2(R_m), where \Omega_2(R_m) denotes the universal module of second order derivations of R_m, is a rational function under some conditions.

** Keywords: **
Universal module, universal differential operators, Betti series, minimal resolution

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