I actually was mistaken - it really looks strange, but it's difference
by constant after all, my fault. The big difference in form misled me.
Thanks for answering my original question anyway, will keep that in
mind if I find real issue next time.
Anyway, now that I'm playing with it more I wonder... there are other
issues with incomplete gamma or I'm mistaken again (I might be, it's
late already)? For example - it seems that Maxima can calculate
derivative, but Sage cannot:
sage: integrate(s^2*exp(-(a+b)*s^2 ), s).diff(s)
-s^4*D[1](gamma)(3/2, (a + b)*s^2)/(sqrt(a + b)*(s^2)^(3/2)) +
3/2*s^4*gamma(3/2, (a + b)*s^2)/((a + b)^(3/2)*(s^2)^(5/2)) -
3/2*s^2*gamma(3/2, (a + b)*s^2)/((a + b)^(3/2)*(s^2)^(3/2))
but maxima for sure knows how to evaluate derivative of incomplete gamma:
(%i8) diff(gamma_incomplete(a,b),b);
a - 1 - b
(%o8) - b %e
other thing, when doing:
sage: assume(A<B)
sage: integrate(s^2 * exp(- (a+b) * s^2 ), s, A, B)
1/2*sqrt(a + b)*A^3*gamma(3/2, (a + b)*A^2)/((a^2 + 2*a*b +
b^2)*abs(A)^3) - 1/2*sqrt(a + b)*B^3*gamma_incomplete(3/2, (a +
b)*B^2)/((a^2 + 2*a*b + b^2)*abs(B)^3)
I noticed that once gamma(a,b) is used, and other time
gamma_incomplete(a,b) instead, while in Maxima in both places there is
gamma_incomplete (tested with 4.6rc0+ecl/maxima update and 4.5.3).
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