Solve Integral with Modified Bessel Function

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SUMMARY

The integral discussed is defined as \(\int_0^{\infty}\text{e}^{-p\gamma}\,\left(\gamma^2+\gamma\right)^{b/2}\,K_b\left(2\,\alpha\,\sqrt{\gamma^2+\gamma}\right)\,d\gamma\), where \(K_b\) represents the modified Bessel function of the second kind of order \(b\). The consensus among participants is that numerical methods are the most viable approach for solving this integral, given its complexity. No analytical solutions were proposed, emphasizing the necessity of numerical integration techniques for evaluation.

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  • Understanding of modified Bessel functions, specifically \(K_b\) functions.
  • Familiarity with numerical integration techniques.
  • Knowledge of integral calculus, particularly improper integrals.
  • Experience with mathematical software capable of numerical computation, such as MATLAB or Python's SciPy library.
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EngWiPy
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Hello,

Is there any way to solve this integral:

[tex]\int_0^{\infty}\text{e}^{-p\gamma}\,\left(\gamma^2+\gamma\right)^{b/2}\,K_b\left(2\,\alpha\,\sqrt{\gamma^2+\gamma}\right)\,d\gamma[/tex]

where [tex]K_v(.)[/tex] is the modified Bessel function of the second kind and [tex]v^{\tex{th}}[/tex] order.??

Thanks in advance
 
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The only way that I would attempt to solve that integral is numerically.
 

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