[Maxima-bugs] [ maxima-Bugs-3292033 ] error in integrating exp(-x)*sinh(sqrt(x))

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Bugs item #3292033, was opened at 2011-04-23 18:24
Message generated for change (Comment added) made by aleksasd
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Category: Lisp Core - Integration
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: https://www.google.com/accounts ()
Assigned to: Nobody/Anonymous (nobody)
Summary: error in integrating exp(-x)*sinh(sqrt(x))

Initial Comment:
Maxima 5.24.0 http://maxima.sourceforge.net
using Lisp SBCL 1.0.24
(%i3) integrate(exp(-x)*sinh(sqrt(x)),x,0,inf);
(%o3)                                  0
(%i4) quad_qagi(exp(-x)*sinh(sqrt(x)),x,0,inf);
(%o4)         [1.137937897234377, 5.171862937913829e-11, 345, 0]


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Comment By: Aleksas (aleksasd)
Date: 2011-05-18 21:20

Message:
solving with Maxima 5.24.0:
 Dwight  Tables of integrals 862.04
(%i1) declare(integrate,linear)$ assume(y>0)$
(%i3) S:'integrate(exp(-x)*sinh(sqrt(x)),x,0,inf)$
(%i4) exponentialize(%);
(%o4) integrate((%e^sqrt(x)-%e^(-sqrt(x)))*%e^(-x),x,0,inf)/2
(%i5) expand(%);
(%o5)
integrate(%e^(sqrt(x)-x),x,0,inf)/2-integrate(%e^(-x-sqrt(x)),x,0,inf)/2
(%i6) S1:changevar(%, y=sqrt(x), y, x);
(%o6) integrate(y*%e^(y-y^2),y,0,inf)-integrate(y*%e^(-y^2-y),y,0,inf)
(%i10) changevar(part(S1,1),2*y-1=z,z,y)+
changevar(part(S1,2),2*y+1=z,z,y);
(%o10)
integrate((z+1)*%e^(-(z^2-1)/4),z,-1,inf)/4-integrate((z-1)*%e^(-(z^2-1)/4),z,1,inf)/4
(%i8) ev(%, nouns),ratsimp;
(%o8) (%e^(1/4)*sqrt(%pi))/2
(%i9) float(%), numer;
(%o9) 1.137937897234373
 
Where is the error?
wrong:
(%i1) R:integrate(y*%e^(y-y^2),y,0,inf);
(%o1)
(%e^(1/4)*gamma_incomplete(1,1/4))/2-(%e^(1/4)*gamma_incomplete(1/2,1/4))/4
(%i2) float(R), numer;
(%o2) 0.22717931961748
(%i3) quad_qagi(y*%e^(y-y^2), y, 0, inf);
(%o3) [1.365117216851849,7.6857545173630158*10^-10,165,0]
 
correct:
(%i4) R1:integrate(y*%e^(-y-y^2),y,0,inf);
(%o4)
(%e^(1/4)*gamma_incomplete(1,1/4))/2-(%e^(1/4)*gamma_incomplete(1/2,1/4))/4
(%i5) float(R1), numer;
(%o5) 0.22717931961748
(%i6) quad_qagi(y*%e^(-y-y^2), y, 0, inf);
(%o6) [0.22717931961748,1.4118104693665376*10^-9,135,0]

                                Aleksas D

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