Evaluate integrals using modified Bessel function of the second kind

In summary, the speaker is asking for help with understanding how to calculate the integral \int_k^\inf \frac{z^2\sqrt{z^2-k^2}}{e^z+1}dz, as they have encountered similar situations while reading papers and textbooks. They apologize for double posting and ask for guidance on where to properly post their question.
  • #1
mjka
4
0
Hi guys,

I encountered it many times while reading some paper and textbook, most of them just quote the final result or some results from elsewhere to calculate the one in that context.

So I'm not having a general idea how to do this, especially this one

[itex]\int_k^\inf \frac{z^2\sqrt{z^2-k^2}}{e^z+1}dz[/itex]

I really appreciate any help. Thank you!
 
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  • #2
Please read the forum rules. Double posts are not allowed.
 
  • #3
phinds said:
Please read the forum rules. Double posts are not allowed.

My apology but I'm a little bit confused about where to post this topic. I'm sorry.
 

FAQ: Evaluate integrals using modified Bessel function of the second kind

What is the modified Bessel function of the second kind?

The modified Bessel function of the second kind, denoted as Kν(x), is a special function used in mathematics and physics to solve integrals involving exponential functions.

How is the modified Bessel function of the second kind evaluated?

The modified Bessel function of the second kind can be evaluated using various methods, such as series expansions, recurrence relations, and integral representations. In some cases, special algorithms and software can also be used to efficiently evaluate these functions.

What are the properties of the modified Bessel function of the second kind?

The modified Bessel function of the second kind has several important properties, such as being a solution to certain differential equations, having a logarithmic singularity at the origin, and satisfying certain recurrence relations. It also has a complex-valued argument and can take on both real and complex values.

What are the applications of the modified Bessel function of the second kind?

The modified Bessel function of the second kind has many applications in physics, engineering, and other fields of science. It is commonly used to solve problems involving heat transfer, diffraction, and oscillatory systems. It also has applications in probability, statistics, and signal processing.

How does the modified Bessel function of the second kind differ from the regular Bessel function?

The modified Bessel function of the second kind is a generalization of the regular Bessel function, also known as the Bessel function of the first kind. While the regular Bessel function has a singularity at the origin, the modified Bessel function has a logarithmic singularity. Additionally, the modified Bessel function can take on complex values, while the regular Bessel function is purely real.

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