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Find Inverse Laplace Transformation of the given function?

Posted 4 years ago

Consider the following code:

InverseLaplaceTransform[1/(s - s^(\[Alpha] + 1) - \[Lambda]), s, 
      t] // FullSimplify
POSTED BY: Surath Ghosh
2 Replies

Using:

$$\sum _{j=0}^{\infty } -s^{(1+j) (-1-\alpha )} (s-\lambda )^j=-\frac{1}{-s+s^{1+\alpha }+\lambda }$$

then we have:

 Sum[FullSimplify[
   InverseLaplaceTransform[-s^((1 + 
         j) (-1 - \[Alpha])) (s - \[Lambda])^j, s, t], 
   Assumptions -> {t > 0, \[Lambda] > 0, \[Alpha] > 0}], {j, 0, 
   Infinity}]

$$\sum _{j=0}^{\infty } -t^{(1+j) \alpha } \, _1\tilde{F}_1(-j;1+\alpha +j \alpha ;t \lambda )$$

I doubt there's a closed form for the series.

Regards M.I.

POSTED BY: Mariusz Iwaniuk

Thank you very much Sir. Closed form is not issue.

POSTED BY: Surath Ghosh
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