I have used method of moment generating functions to derive the chi-squared distribution with k degrees of freedom and obtained the following result: $\frac{1}{(1-2s)^{k/2}} $ I want to obtain the PDF of the function (i. e. take the inverse laplace transform). Wolfram seems to give the correct answer, but I'm interested in how to take this transform "by hand". I know that the formula for the inverse is given by complex integral, but I'm not able to derive the desired formula myself.
2026-04-03 01:50:53.1775181053
Taking the inverse Laplace transfrom of non-rational functions
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