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 Web Resource. https://mathworld.wolfram.com/Laplace-StieltjesTransform.html