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removed "Thanks in Advantage"
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edit approved Jun 15, 2023 at 0:35
Starship
edit approved Jun 15, 2023 at 0:35
Starship
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I would need some help to work with the following integral:

$$f(x) = \int_2^\infty \log (1-x^t) dt ,\ \ \ \ \ \ \ \ \ |x|<1$$

I would like to get a closed form or something similar (which seems to be impossible), but any other type of exact equivalent expression to work with would be great.

Making a change of variables seems not to help much. I also tried to evaluate it as a complex integral, but the path of integration $[2, \infty)$ is not the easiest to work with.

Any idea will be welcomed. Thank you in advantage.

I would need some help to work with the following integral:

$$f(x) = \int_2^\infty \log (1-x^t) dt ,\ \ \ \ \ \ \ \ \ |x|<1$$

I would like to get a closed form or something similar (which seems to be impossible), but any other type of exact equivalent expression to work with would be great.

Making a change of variables seems not to help much. I also tried to evaluate it as a complex integral, but the path of integration $[2, \infty)$ is not the easiest to work with.

Any idea will be welcomed. Thank you in advantage.

I would need some help to work with the following integral:

$$f(x) = \int_2^\infty \log (1-x^t) dt ,\ \ \ \ \ \ \ \ \ |x|<1$$

I would like to get a closed form or something similar (which seems to be impossible), but any other type of exact equivalent expression to work with would be great.

Making a change of variables seems not to help much. I also tried to evaluate it as a complex integral, but the path of integration $[2, \infty)$ is not the easiest to work with.

Any idea will be welcomed.

the question title is inconsistent with the question in that n was used in the title but t was used in the question, I fixed this
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edit approved Aug 13, 2018 at 0:51
Mathew
edit approved Aug 13, 2018 at 0:51
Mathew
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Integral of $\log(1-x^nx^t)$ with respect to $n$$t$

added 21 characters in body
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user3141592
user3141592
  • 1.9k
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I would need some help to work with the following integral:

$$f(x) = \int_2^\infty \log (1-x^t) dt ,\ \ \ \ \ \ \ \ \ |x|<1$$

I would like to get a closed form or something similar (which seems to be impossible), but any other type of exact equivalent expression to work with would be great.

Making a change of variables seems not to help much. I also tried to evaluate it as a complex integral, but the path of integration $[2, \infty)$ is not the easiest to work with.

Any idea will be welcomed. Thank you in advantage.

I would need some help to work with the following integral:

$$f(x) = \int_2^\infty \log (1-x^t) dt ,\ \ \ \ \ \ \ \ \ |x|<1$$

I would like to get a closed form (which seems to be impossible), but any other type of exact equivalent expression to work with would be great.

Making a change of variables seems not to help much. I also tried to evaluate it as a complex integral, but the path of integration $[2, \infty)$ is not the easiest to work with.

Any idea will be welcomed. Thank you in advantage.

I would need some help to work with the following integral:

$$f(x) = \int_2^\infty \log (1-x^t) dt ,\ \ \ \ \ \ \ \ \ |x|<1$$

I would like to get a closed form or something similar (which seems to be impossible), but any other type of exact equivalent expression to work with would be great.

Making a change of variables seems not to help much. I also tried to evaluate it as a complex integral, but the path of integration $[2, \infty)$ is not the easiest to work with.

Any idea will be welcomed. Thank you in advantage.

Source Link
user3141592
user3141592
  • 1.9k
  • 12
  • 25