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In this article we construct a function with infinitely many vanishing(generalized) moments. This is motivated by an application to the Taylorlettransform which is based on the continuous shearlet transform. It can detectcurvature and other higher order geometric information of singularities inaddition to their position and the direction. For a robust detection of thesefeatures a function with higher order vanishing moments, $\int_\mathbb{R}g(x^k)x^m dx = 0$, is needed. We show that the presented construction producesan explicit formula of a function with infinitely many vanishing moments ofarbitrary order and thus allows for a robust detection of certain geometricfeatures. The construction has an inherent connection to q-calculus, the Eulerfunction and the partition function.

A space-based method for the generation of a Schwartz function with  infinitely many generalized vanishing moments with applications in image  processing