- #1

Hepth

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Limit[Integrate[(1 - 2 x)/x^2, {x, a, b}], a -> 0]

Integrate[(1 - 2 x)/x^2, {x, 0, b}]

The first one gives infinity, the second a closed solution, though technically they should be the same, right?

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- #1

Hepth

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Limit[Integrate[(1 - 2 x)/x^2, {x, a, b}], a -> 0]

Integrate[(1 - 2 x)/x^2, {x, 0, b}]

The first one gives infinity, the second a closed solution, though technically they should be the same, right?

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Which version of Mma are you using and what is the closed solution the second one gives you?

The integrand goes like 1/x^2 + 1/x as x->0 and so diverges, and as Wolfram|Alpha says, the Cauchy principle value is +Infinity.

In Mma8 the first expression returns

ConditionalExpression[Indeterminate, b >= 0]

(which seems like a mistake to me... what's b>=0 got to do with anything?)

While the second gives a warning about nonconvergence and keeps the expression unevaluated.

ConditionalExpression is new in Mma8. So Mma7 generates conditions for when the integral over {x, a, b} converges in the form of an If[] statement. I gave up waiting for it to take the limit of the resulting expression. Mma7 has the same behaviour as Mm8 for the integral over {x, 0 b}.

And yes, assuming that b is Real, both expressions should yield +Infinity

The integrand goes like 1/x^2 + 1/x as x->0 and so diverges, and as Wolfram|Alpha says, the Cauchy principle value is +Infinity.

In Mma8 the first expression returns

ConditionalExpression[Indeterminate, b >= 0]

(which seems like a mistake to me... what's b>=0 got to do with anything?)

While the second gives a warning about nonconvergence and keeps the expression unevaluated.

ConditionalExpression is new in Mma8. So Mma7 generates conditions for when the integral over {x, a, b} converges in the form of an If[] statement. I gave up waiting for it to take the limit of the resulting expression. Mma7 has the same behaviour as Mm8 for the integral over {x, 0 b}.

And yes, assuming that b is Real, both expressions should yield +Infinity

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I get Simon's results also. Essentially both methods diverge.

- #4

Hepth

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So when I run it from a fresh start, I get that they both diverge. If I do some of my other code, NONE OF WHICH uses a,b, or x, I get this:

And if I change x-> something random and b-> something random, it does the SAME thing.

EDIT::

I Think I found the problem, there must be something in Feyncalc. If I do:

<< HighEnergyPhysics`FeynCalc`;

just to load it, then do the integrals , it gives the weird responses... I wonder if there is something in its definitions to handle the N-dimensional divergent integrals that is messing with this.

- #5

Hepth

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Here's what I get:

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The output you obtain after loading FeynCalc is the same as

Integrate[(1 - 2 x)/x^2, {x, 0, b}, GenerateConditions -> False]

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I just downloaded the latest version of the http://www.feyncalc.org/" [Broken] package and did a quick

find . -exec grep -l "GenerateConditions" {} \;

and the only files that turned up in the latest version of FeynCalc was the FeynCalcBook.nb and /fctables/Integrate3.m. But it only applied to a specific PolyLog integral... So I'm not sure what's causing the problem.

You can similarly find every file that contains the string "Integrate" - but a quick look at these does not show anything obvious....

Finally, I ran the same sequence of commands you gave in your screenshots in both Mma7 and Mma8 and did not reproduce your results...

Can you load FeynCalc and run "Options[Integrate, GenerateConditions]" to see if it returns the default "GenerateConditions->Automatic"?

I assume that it must be set to False, because otherwise your Out[8] would have the same conditions attached to it as your Out[3]. Then it's just a matter of tracking down what setting you've made in you FeynCalc install that would do this. Try running the "find ..." command I gave above in your FeynCalc directory.

find . -exec grep -l "GenerateConditions" {} \;

and the only files that turned up in the latest version of FeynCalc was the FeynCalcBook.nb and /fctables/Integrate3.m. But it only applied to a specific PolyLog integral... So I'm not sure what's causing the problem.

You can similarly find every file that contains the string "Integrate" - but a quick look at these does not show anything obvious....

Finally, I ran the same sequence of commands you gave in your screenshots in both Mma7 and Mma8 and did not reproduce your results...

Can you load FeynCalc and run "Options[Integrate, GenerateConditions]" to see if it returns the default "GenerateConditions->Automatic"?

I assume that it must be set to False, because otherwise your Out[8] would have the same conditions attached to it as your Out[3]. Then it's just a matter of tracking down what setting you've made in you FeynCalc install that would do this. Try running the "find ..." command I gave above in your FeynCalc directory.

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- #8

Hepth

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In[1]:= Options[Integrate,GenerateConditions]

Out[1]= {GenerateConditions->Automatic}

In[2]:= <<HighEnergyPhysics`FeynCalc`;

During evaluation of In[2]:= Set::wrsym: Symbol MonomialList is Protected. >>

During evaluation of In[2]:= DumpGet::bgbf: File C:\Program Files\Wolfram Research\Mathematica\7.0\AddOns\Applications\HighEnergyPhysics\Tarcer\tarcer25.mx cannot be loaded, it is corrupted or is written on a different machine. >>

In[3]:= Options[Integrate,GenerateConditions]

Out[3]= {GenerateConditions->False}

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