I am just looking for a proof or help to solve the Laplace Transform that:
f(t^α) = [ Γ(α+1) ] / [ s^(α+1) ]
I dont even know where to begin working on this and any help would be greatly appreciated.
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You need the definition of the Laplace transform and make a substitution as follows:
You can rewrite this after the substitution as:
Which can be written using the definition of the Gamma function to the required result.
I'm not seeing how substituting in u for st is turning the t into a u.
Originally Posted by eeverett1 I'm not seeing how substituting in u for st is turning the t into a u. .
Now let so then .
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