A Laplace-Stieltjes transform is an integral transform which is often written as an ordinary Laplace transform involving the delta function. The Laplace transform and Dirichlet series are special cases of the Laplace-Stieltjes transform (Apostol 1997, p. 162).
Laplace-Stieltjes Transform
See also
Dirichlet Series, Laplace TransformExplore with Wolfram|Alpha
References
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 1029, 1972.Apostol, T. M. Modular Functions and Dirichlet Series in Number Theory, 2nd ed. New York: Springer-Verlag, p. 162, 1997.Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, 1953.Widder, D. V. The Laplace Transform. Princeton, NJ: Princeton University Press, 1941.Referenced on Wolfram|Alpha
Laplace-Stieltjes TransformCite this as:
Weisstein, Eric W. "Laplace-Stieltjes Transform." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Laplace-StieltjesTransform.html