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We investigate the first cohomology space associated with the embedding ofthe Lie superalgebra $\cK(2)$ of contact vector fields on the (1,2)-dimensionalsupercircle $S^{1\mid 2}$ in the Lie superalgebra $\cS\Psi \cD \cO(S^{1\mid2})$ of superpseudodifferential operators with smooth coefficients. FollowingOvsienko and Roger, we show that this space is ten-dimensional with only evencocycles and we give explicit expressions of the basis cocycles.Comment: Accepted for publication at the Journal of Nonlinear Mathematical  Physic

On the Cohomology of the Lie Superalgebra of Contact Vector Fields on S1|2