simplify_sum error
- Subject: simplify_sum error
- From: Aleksas Domarkas
- Date: Tue, 13 Mar 2012 09:00:28 +0200
I calculate integral
integrate(sqrt(x)*sqrt(1+x^2), x, 0, 1);
The answer should be
(%i1) 2/3*hypergeometric([-1/2,3/4],[7/4],-1);
(%o1) (2*hypergeometric([-1/2,3/4],[7/4],-1))/3
(%i2) a1:float(%), numer;
(%o2) 0.79248561598088
(%i3) quad_qags(sqrt(x)*sqrt(1+x^2), x, 0, 1);
(%o3) [0.79248561598088,1.0454970222895099*10^-12,231,0]
(%i4) load(simplify_sum)$
(%i5) sqrt(x)*niceindices(powerseries(sqrt(1+x^2),x,0));
(%o5) (2*sqrt(x)*sum(x^(2*i)/beta(3/2-i,i+1),i,0,inf))/3
(%i6) intosum(%);
(%o6) sum((2*x^(2*i+1/2))/(3*beta(3/2-i,i+1)),i,0,inf)
(%i7) integrate(%,x);
(%o7) (2*sum(x^(2*i+3/2)/(beta(3/2-i,i+1)*(2*i+3/2)),i,0,inf))/3
(%i8) sol:ev(%,x=1)-ev(%,x=0);
(%o8) (2*sum(1/(beta(3/2-i,i+1)*(2*i+3/2)),i,0,inf))/3
(%i9) simplify_sum(sol);
expt: undefined: 0 to a negative exponent.
#0:
to_hypergeometric1(expr=2/((4*i+3)*beta(i+1,-(2*i-3)/2)),var=i,lo=0,hi=inf)(simplify_sum.mac
line 781)
#1:
to_hypergeometric(expr=2/((4*i+3)*beta(i+1,-(2*i-3)/2)),var=i,lo=0,hi=inf)(simplify_sum.mac
line 743)
#2:
simplify_sum(expr='sum(1/(beta(3/2-i,i+1)*(2*i+3/2)),i,0,inf))(simplify_sum.mac
line 292)
-- an error. To debug this try: debugmode(true);
(%i10) subst(inf=1000,sol)$
(%i11) ev(%, nouns)$
(%i12) float(%), numer;
(%o12) 0.79248561375435
(%i13) a1;
(%o13) 0.79248561598088
Aleksas D