Summary
A simple algorithm of finding inverse Laplace transforms of an exponential form is devised. To avoid lengthy and tedious calculations of derivatives, two functionsS andT are introduced; it is shown that derivatives ofS andT with respect to parameters are expressed by combinations ofS andT. The formulas for derivatives ofS andT can be applied repeatedly to obtain a class of inverses.
Sommaire
On développe un algorithme simple pour trouver la transformée inverse de Laplace des fonctions à forme exponentielle. Pour éviter des calculs longs et ennuyeux, on introduit deux fonctionsS etT et on démontre que les derivées deS et deT par rapport aux paramètres s'expriment par des combinaisons deS et deT. On peut appliquer les formules des derivées deS et deT à plusieurs reprises pour obtenir une classe des inverses.
References
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Hetnarski, R.B. An algorithm for generating some inverse Laplace transforms of exponential form. Journal of Applied Mathematics and Physics (ZAMP) 26, 249–253 (1975). https://doi.org/10.1007/BF01591514
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DOI: https://doi.org/10.1007/BF01591514