New Laplace transforms of Kummer’s confluent hypergeometric functions

In this paper we aim to show how one can obtain so far unknown Laplace transforms of three rather general cases of Kummer’s confluent hypergeometric function 1F1(a;b;x)1F1(a;b;x) by employing generalizations of Gauss’s second summation theorem, Bailey’s summation theorem and Kummer’s summation theorem obtained earlier by Lavoie, Grondin and Rathie. The results established may be useful in theoretical physics, engineering and mathematics.