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# Laplace transform of Power function

Posted 9 years ago
 Hello, I was trying to use Wolfram Alpha engine to transform a power function using laplace transform and then inverse using inverse laplace transform. The function is: D(t) = a*t^b + c  ('t' is the initial variable, 's' is the transform variable and 'a', 'b', and 'c' are constant parameters) When I transfer it using Laplace Transform, I got this results: a s^(-b-1) Gamma(b+1)+c/s  However, when I try to inverse the result function using the formula: 1/s^2 as shown below: 1/[s^2*(a s^(-b-1) Gamma(b+1)+c/s)]  The engine doesn't give me any results. as shown in the below image: I keep clicking on 'Solve' button but with no response. Can anyone help me in finishing this? Thank you..
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Posted 9 years ago
 Hi, Thanks Sean for replying.. Actually, I am trying to follow another example I found. The example is trying to solve the below equation using laplace transform: So, he got this: By using this formula: he became able to identify this: And using the inverse laplace transform he got this: Then he compare it with the original relaxation modulus: To identify each part of the equation as follows: So, when I tried to follow the above steps, I couldn't inverse the results from laplace transform after multiplying by 1/s^2. I appreciate your help and explaination..
Posted 9 years ago
 What result are you expecting for the Inverse Laplace Transform of 1/[s^2*(a s^(-b-1) Gamma(b+1)+c/s)]?It doesn't show a result becuase it doesn't find any result. Are you sure you're not looking for the inverse transform of (1/s^2)(a s^(-b-1) Gamma(b+1)+c/s) instead? Are you looking for the convolution of t and a*t^b + c?