Table of Integrals: Solving \int_0^{\infty}x^A\,(x^2+x)^{B/2}\,e^{-Cx}\,K_{(B)}

[EngWiPy]

Hello,
During my derivation, I am faced with the following integral:

$$\int_0^{\infty}x^A\,(x^2+x)^{B/2}\,e^{-Cx}\,K_{(B)}\left(2\,\alpha\,\sqrt{x^2+x}\right)\,dx$$

where A, B, and C are positive integers, $$K_{(B)}$$ is the $$B^{th}$$ order modified bessel function of the second kind. I am intending to find an equivalent integral in the table of integrals. Can anyone help me, please?

 

[aaryan0077]

Hello,
During my derivation, I am faced with the following integral:

$$\int_0^{\infty}x^A\,(x^2+x)^{B/2}\,e^{-Cx}\,K_{(B)}\left(2\,\alpha\,\sqrt{x^2+x}\right)\,dx$$

where A, B, and C are positive integers, $$K_{(B)}$$ is the $$B^{th}$$ order modified bessel function of the second kind. I am intending to find an equivalent integral in the table of integrals. Can anyone help me, please?

I think this forum is for general discussions rather than homework help, you should post this in homework help section,
here
https://www.physicsforums.com/forumdisplay.php?f=152"

 

[CRGreathouse]

I think this forum is for general discussions rather than homework help

Graduate-level homework is acceptable here. This looks like it might fit -- I certainly didn't do hairy integrals with Bessel functions as an undegrad.

 

[aaryan0077]

Graduate-level homework is acceptable here. This looks like it might fit -- I certainly didn't do hairy integrals with Bessel functions as an undegrad.

Okay, whatever you say.