Evaluate integrals using modified Bessel function of the second kind

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SUMMARY

The discussion focuses on evaluating integrals that involve the modified Bessel function of the second kind, specifically the integral \int_k^\inf \frac{z^2\sqrt{z^2-k^2}}{e^z+1}dz. Participants express a lack of general understanding regarding the methodology for solving such integrals, as many resources only provide final results without detailed explanations. The conversation highlights the need for a clearer framework or approach to tackle these types of integrals effectively.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with modified Bessel functions
  • Knowledge of asymptotic analysis
  • Experience with mathematical software for symbolic computation
NEXT STEPS
  • Research methods for evaluating integrals involving modified Bessel functions
  • Learn about asymptotic expansions for integrals
  • Explore mathematical software tools like Mathematica or MATLAB for integral evaluation
  • Study the properties and applications of the modified Bessel function of the second kind
USEFUL FOR

Mathematicians, physicists, and engineers who are involved in advanced calculus, particularly those working with integrals in theoretical contexts or applied mathematics.

mjka
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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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Please read the forum rules. Double posts are not allowed.
 
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.
 

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