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Groups > comp.soft-sys.math.maple > #306

How do I Show Equal

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I am trying to duplicate a Maxima proof.

#######################################
# Theorum
# for any real k,a,b
# integrate(exp(x)*x^k,x=a..b)
#    =exp(1)^(-I*Pi*k)*(gamma_incomplete(k+1,-b)
#     - gamma_incomplete(k+1,-a))
# maxima proof
# S:'integrate(exp(x)*x^k,x)';
# S1:ev(S, nouns);
# subst(-x=exp(%i*pi)*x,S1);
# /* From Newton-Leibnitz formula S is equal */
# subst(x=b,%)-subst(x=a,%);
# radcan(%);
# subst(pi=%pi,%);
restart;
S:=integrate(exp(x)*x^k,x);  # this seems to include the ev(S, nouns)
soln:=exp(1)^(-I*Pi*k)*(GAMMA(k+1,-b)-GAMMA(k+1,-a));
# from I should be able to reduce to soln
subs(x=b,S) - subs(x=a,S);

But, my lack of Maple expertise prevents reduction of this expression to 
soln.

How do I do this?

Tom Dean

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How do I Show Equal "Thomas D. Dean" <tomdean@speakeasy.org> - 2012-01-13 12:14 -0800
  Re: How do I Show Equal Axel Vogt <&noreply@axelvogt.de> - 2012-01-14 09:31 +0100

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