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RSS Feed for Wolfram Community showing any discussions in tag Calculus sorted by activeDetermine inverse Laplace transforms of these expressions?
https://community.wolfram.com/groups/-/m/t/2163007
Hi, I have a new problem with determining inverse Laplace transforms. The following code generates a series expansion of a certain expression, and then attempts to calculate inverse Laplace transforms of the successive series coeffcients. The coefficients are functions of the Laplace variable s that appear rather hard (for me) to be expressed by any recursive formula, so that I do not see a way to represent them in an alternative way. The problem is that the InverseLaplaceTransform[] command manages to invert only the first three coefficients, and I need at least 40. I believe all these inverses should contain the DawsonF[] function. Application of Apart[] makes things even worse, and diminishes the number of inverted coefficients. Is there any other method that could be applied to rearrange the expressions in some systematic way so that the inverses can be obtained?
Leslaw.
The code:
nmax=5;
F[s_]:=(((1+s)^2+3*s^(3/2)*(1+s)^(1/2)*th-4*s*(1+s)*th+3*s^(1/2)*(1+s)^(3/2)*th+s^2*th^2))/
(8 (s^(3/2)*(1+s)^(1/2)*((1+s)^(1/2)+s^(1/2)*th)^3));
ser0=Simplify[Series[F[s],{th,0,nmax}]];
coeffs0=Table[SeriesCoefficient[ser0,n],{n,0,nmax}];
coeffs1=InverseLaplaceTransform[coeffs0,s,t]Leslaw Bieniasz2021-01-14T19:51:12Z