What is the difference between moment generating function and Laplace transform?

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S P Bhairat

Basically you can go through the following article and references therein.

Maged G. Bin-Saad

You may read the following two papers

(1)Preservation Properties of the Laplace Transform and Moment Generating Function Ordering of Residual Life and Inactivity Time

http://booksc.org/book/39743386/4ae94b

(2) On the Use of Generating Functions and Laplace Transforms in Applied Probability Theory

http://booksc.org/book/35220530/438142