Incomplete Gamma Function



Am Donnerstag, den 13.05.2010, 11:08 -0400 schrieb Burgess, Don:
> Is the implementation of the Incomplete Gamma Function in Maxima
> unfinished?

Thank you very much for your example. Unfortunately, Maxima can not
solve your type of definite integral.

Maxima knows the indefinite integral in terms of the gamma_incomplete
function:

(%i1) integrate(exp(-x)/x-exp(-2*x)/x,x);
(%o1) gamma_incomplete(0,2*x)-gamma_incomplete(0,x)

Furthermore, Maxima can simplify the result in terms of the Exponential
Integral Ei:

(%i2) integrate(exp(-x)/x-exp(-2*x)/x,x),gamma_expand:true,radcan;
(%o2) expintegral_ei(-x)-expintegral_ei(-2*x)

But Maxima does not know your definite integral:

(%i10) integrate(exp(-x)/x-exp(-2*x)/x,x,0,inf);
(%o10) -'limit(gamma_incomplete(0,2*x)-gamma_incomplete(0,x),x,0,plus)

Further work is needed to get more definite integrals.

Dieter Kaiser