What is the Laplace Transform of a Gaussian Distribution?

[stefanfuglsang]

I need a large table of Laplace transforms, do you know any good ones? Format HTML, Pdf, Ps, Latex or Word (?)

Extra question: what is the Laplace transform of a Gaussian (normal distribution), with mean m and standard deviation s (assume equal to zero for t<0)?

 

[chroot]

Well, I went to google, typed in "table laplace transforms" and the very first link was:

http://www.vibrationdata.com/Laplace.htm

Whew -- that was tough.

- Warren

 

[fourier jr]

I need a large table of Laplace transforms, do you know any good ones? Format HTML, Pdf, Ps, Latex or Word (?)

Extra question: what is the Laplace transform of a Gaussian (normal distribution), with mean m and standard deviation s (assume equal to zero for t<0)?

why not make your own table? good integration practice hehe

 

[stefanfuglsang]

I also know how to use Google - but you do not answer my question,
maybe I should define "Large" as more than, say, 150 transforms.

I do not need to practice integration

 

[quantumdude]

I also know how to use Google - but you do not answer my question,
maybe I should define "Large" as more than, say, 150 transforms.

I typed "large table laplace transforms" into Google. Check out this link. It has 129 Laplace transform formulas.

http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP?Res=200&Page=1019

It was the second link that came up. The first was this thread.

 

[eJavier]

Schaum's intro to Laplace transforms has like 300 laplace transforms listed on a big table.

 

[eJavier]

I need a large table of Laplace transforms, do you know any good ones? Format HTML, Pdf, Ps, Latex or Word (?)

Extra question: what is the Laplace transform of a Gaussian (normal distribution), with mean m and standard deviation s (assume equal to zero for t<0)?

If it helps, the LT of the error function \frac{2}{\pi^{\frac{1}{2}} }\int_0^t e^{-u^2} du is \frac {1}{s(s+1)^{1/2}}

And since you can always work with the N(0,1) distribution instead of the more general N(m, sigma^2) I think you'll find the aforementioned result useful. If you need the derivation of the Lt just ask.