New identities involving the Laplace and the \({\mathcal L}_2\)-transforms and their applications
The integral transform \[ {\mathcal L}_2\bigl\{f(x); y\bigr\}= \int^\infty_0 x\exp(-x^2y^2) f(x)dx=\textstyle{1\over 2} {\mathcal L}_2\bigl\{f(x^{1/2}); y^2\bigr\} \] is considered. Identities are obtained which involve this, the Laplace, and the Widder transforms. As a consequence of these identities, the evaluations are made of a number of specific integrals, many of which involve the error functions.
scientific article; zbMATH DE number 1311101