Nasser M. Abbasi wrote:
>
> question came up if Fricas Gamma(a,x) is the upper or lower incomplete
> gamma function. I am almost sure it is the upper. But wanted to make sure,
> since I could not evaluate it numerically to verify and could not find the
> definition of it in Fricas.
>
> (it would be really nice if help in Fricas shows the actual mathematical
> formula definition of the special functions and not just give the name).
>
> https://en.wikipedia.org/wiki/Incomplete_gamma_function
>
> and from http://fricas.github.io/api/FunctionalSpecialFunction.html
>
> "Gamma: (F, F) -> F
>
> Gamma(a, x) returns the incomplete Gamma function applied to a and x"
Well,
(1) -> D(Gamma(a, x), x)
- x a - 1
(1) - %e x
Type: Expression(Integer)
which only makes sense for "upper" variant. Also, it is "Gamma" and
not "gamma" (FriCAS distinguishes the two and usually would use
lowercase variant of spelling, but in this case uppercase is used
to limit confusion).
--
Waldek Hebisch
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