Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2007
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2007

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: GenerateConditions->False gives fine result!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73876] Re: GenerateConditions->False gives fine result!
  • From: Bhuvanesh <lalu_bhatt at yahoo.com>
  • Date: Fri, 2 Mar 2007 06:39:36 -0500 (EST)

This is because the integral does in fact diverge in the Riemann sense. Taking the simpler example with {t->3, x->2}:

In[1]:= integrand = q/(E^(2*I*q)*Sqrt[q^2 + 9]);

In[2]:= Limit[integrand, q->Infinity]

Out[2]= (1 + I) Interval[{-1, 1}]

GenerateConditions->False, in addition to checking convergence and looking for singularities, also does Hadamard-type integrals. Here's another example:

In[1]:= Integrate[1/(x^(1 + I/2)*(1 + x)), {x, 0, 1}]

                                    1
Integrate::idiv: Integral of ---------------- does not converge on {0, 1}.
                              1 + I/2
                             x        (1 + x)

                         1
Out[1]= Integrate[----------------, {x, 0, 1}]
                   1 + I/2
                  x        (1 + x)

In[2]:= Integrate[1/(x^(1 + I/2)*(1 + x)), {x, 0, 1}, GenerateConditions->False] //InputForm

Out[2]//InputForm= (-PolyGamma[0, -I/4] + PolyGamma[0, 1/2 - I/4])/2

Bhuvanesh,
Wolfram Research.


  • Prev by Date: Re: Dll problem
  • Next by Date: Re: Interrupt Service Routines in Mathematica v.5.2?
  • Previous by thread: GenerateConditions->False gives fine result!
  • Next by thread: Re: GenerateConditions->False gives fine result!