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The functions studied in the paper are quaternion-valued functions of aquaternionic variable. It is show that the left slice regular functions andright slice regular functions are related by a particular involution. Therelation between left slice regular functions, right slice regular functionsand intrinsic regular functions is revealed. The classical Laplace transformcan be naturally generalized to quaternions in two different ways, whichtransform a quaternion-valued function of a real variable to a left or rightslice regular quaternion-valued function of a quaternionic variable. The usualproperties of the classical Laplace transforms are generalized to quaternionicLaplace transforms.

Quaternionic slice regular functions and quaternionic Laplace transforms