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Re: Pseudo-Singular Integrals


I don't see what the problem is.  It seems to work just fine:

In[1]:= w = 10^-7;

In[2]:= NIntegrate[-PolyLog[2,-1/y]/(w+y)^4 + Log[(1-y)y/(w+y)] *
        PolyLog[2,-(1-y)/y], {y, 0, 10^-5, 1},
        Method -> DoubleExponential]

                  22
Out[2]= 5.26212 10


BTW, the second term contributes very little:

In[3]:= NIntegrate[-PolyLog[2,-1/y]/(w+y)^4, {y, 0, 10^-5, 1},
        Method -> DoubleExponential]

                  22
Out[3]= 5.26212 10

In[4]:= %%/% - 1

Out[4]= 0.


Jerry B. Keiper
keiper at wri.com
Wolfram Research, Inc.





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