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Gamma function - robmio - 08-06-2020 01:56 PM
Hello everyone, I would like to know how to replace "Gamma(a,0)" and "Gamma(a,infinity)" ("a" equal, for example, to 2, or to 1/5, etc.) with "gamma(a)" and with "0" , respectively.
For example the following approach does not work:
"subst(Gamma (2/3,0), Gamma (a,0), Gamma(a))".
How can I do?
Sincerely, robmio
RE: Gamma function - robmio - 08-06-2020 03:49 PM
For example: laplace(t^(-1/3),t,s) -->
(-s*Gamma(2/3,infinity)+s*Gamma(2/3,0))/(s*(s^(2/3))).
RE: Gamma function - robmio - 08-06-2020 06:14 PM
In HP PRIME, Gamma function can take one argument as "complete" gamma function, or 2 arguments as incomplete gamma function:
Gamma(a) = Gamma(a,0) = int(t^(a-1)*exp(-t),t,0,infinity)
Gamma(a,x) = int(t^(a-1)*exp(-t),t,x,infinity).
In HP PRIME, for example, Gamma(0.5,0) = 1.7724
Gamma(0.5,2) = 0.080647.