What is the Laplace Transform of a Gaussian Distribution?

In summary, Google lead me to ConvertIt.com, which has a table of Laplace transforms with 129 entries. The Lt of the error function is 1/s(s+1)^{1/2}, and can be found using the N(0,1) distribution.
  • #1
stefanfuglsang
6
0
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)?
 
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  • #2
  • #3
stefanfuglsang said:
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 :wink: :tongue2:
 
  • #4
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
 
  • #5
stefanfuglsang said:
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.

:rolleyes:

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. :rofl:
 
  • #6
Schaum's intro to Laplace transforms has like 300 laplace transforms listed on a big table.
 
  • #7
stefanfuglsang said:
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 [tex] \frac{2}{\pi^{\frac{1}{2}} }\int_0^t e^{-u^2} du [/tex] is [tex]\frac {1}{s(s+1)^{1/2}}[/tex]

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.
 
Last edited:

1. What is a Table of Laplace Transforms?

A Table of Laplace Transforms is a mathematical tool used to transform functions from the time domain to the Laplace domain. It is a table that lists common functions and their corresponding Laplace transforms.

2. How is a Table of Laplace Transforms used?

A Table of Laplace Transforms is used to simplify the process of finding the Laplace transform of a function. Instead of having to use the definition of the Laplace transform, which involves integration, one can simply look up the transform in the table.

3. What types of functions are included in a Table of Laplace Transforms?

A Table of Laplace Transforms typically includes common functions such as polynomials, trigonometric functions, exponential functions, and their combinations. It may also include special functions such as the unit step function and the impulse function.

4. How do I read a Table of Laplace Transforms?

A Table of Laplace Transforms typically has two columns - one for the function and one for its Laplace transform. To use the table, find the function you want to transform in the first column and its corresponding transform in the second column.

5. Can a Table of Laplace Transforms be used for inverse Laplace transforms?

No, a Table of Laplace Transforms cannot be used for inverse Laplace transforms. It is only used to find the Laplace transform of a function. To find the inverse Laplace transform, you will need to use other techniques such as partial fraction decomposition or the Bromwich integral.

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