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Feb 18, 2021 at 15:01 comment added Quiet_waters @bathalf15320 I thank you so much, I did not know. Thank you!
Feb 18, 2021 at 14:35 comment added bathalf15320 I must take issue with the claim that the exact function is not known by any people. This is simply not true. The standard formula holds for all values of the parameter. The reason for the restriction in the values of the latter in many tables is that they only consider the transforms of functions. But the expression $s^\alpha$ defines a distribution on the posiitive half-line for any real $\alpha$ and the Laplace tranformation of distributions has been studied in detail, starting with Schwartz in the 50's.
Feb 15, 2021 at 13:30 vote accept Quiet_waters
Feb 15, 2021 at 12:46 answer added Carlo Beenakker timeline score: 3
Feb 15, 2021 at 8:02 history edited gmvh
Added top-level tag
Feb 15, 2021 at 1:47 history asked Quiet_waters CC BY-SA 4.0