title: Computing inverse Laplace transform of Bessel function in Matlab
body: <p>I am trying to evaluate the inverse Laplace transform of a function that includes the modified Bessel function of the second kind, i.e., my function is f_s = sqrt(a*s)*besselk(1,2*sqrt(a*s)), where a is a constant (say a = 0.5) and 's' is defined as a symbol. To evaluate the inverse Laplace transform of this function, I used the built-in Matlab function 'ilaplace' as transV = ilaplace(f_s,s,t), where I want to evaluate my function at 't' = 2. However, the problem I am getting is that the inverse transformed expression transV still contains 's' variable, which I supposed to transform to 't' after the inverse Laplace transform. </p>
  
  <p>Can anyone help me with what is the problem with this approach? I checked the Matlab documentation and still couldn't figure out the solution. I already tried using 'vpa' function as it was suggested in one of the Matlab forums, but that didn't help to get rid of 's'. I am stuck with this and would really appreciate any help on it. </p>
  
  <p>My code is</p>
  
  <pre><code>a = 0.5; t = 2;
  syms s;
  f_s = sqrt(a*s)*besselk(1,2*sqrt(a*s));
  transV = ilaplace(f_s,t); % or transV = vpa(ilaplace(f_s,t)); 
  </code></pre>
  
  <p>With this, the final result transV still has an expression which is a function of 's' although it should be transformed after ilaplace.</p>