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On a generalization of Laplace transform due to E. Krätzel. (English) Zbl 0844.44002
Summary: We study an integral transform introduced by E. Krätzel and denoted by $$L_{\nu,n}$$ that generalizes the well-known Laplace and Meijer transformations. We establish two new real inversion formulas for $$L_{\nu,n}$$. In the first formula we employ differential operators of infinite order and in the second one we use a differential operator which generalizes the Post-Widder operator. We also prove Abelian and Tauberian theorems for the $$L_{\nu,n}$$ transformation.
##### MSC:
 44A15 Special integral transforms (Legendre, Hilbert, etc.) 44A10 Laplace transform