Analyzing an Integral Solution for Exponential Integral with Imaginary Numbers

[EngWiPy]

Hello,

Is this integral solvable in compact form?

[tex]\int_0^{\infty}e^{-j\nu\alpha}E_1^m(-j\nu)\,d\nu[/tex]

where ##E_1(.)## is the exponential integral and ##j=\sqrt{-1}##. I am trying to avoid solving it numerically because its solution won't be the end result.

Thanks

 

[George Jones]

Is this integral solvable in compact form?

I am unfamiliar with notation. What does the ##m## mean in ##E^m_1##? The same as ##E_1 \left( -i\nu \right)^m##, or something else? Once I understand the notation, I will ask Maple to have a go at it.

 

[EngWiPy]

I am unfamiliar with notation. What does the ##m## mean in ##E^m_1##? The same as ##E_1 \left( -i\nu \right)^m##, or something else? Once I understand the notation, I will ask Maple to have a go at it.

Yes, m is an integer and ##E_1^m(x)=\left(E_1(x)\right)^m##

 

[George Jones]

Arbitrarily, I set ##\alpha = 1## and ##m=3##, and Maple not did give a closed form solution for this special case.

 

[EngWiPy]

Hello,

I have this function in an integration ##E_1^m(z)##, which is the exponential integral to the power ##m##. I am looking to write it in a way, such that I can evaluate in compact form the following integration

[tex]\int_0^{\infty}e^{-jxt}E_1^m(-jt)\,dt[/tex]

to avoid calculating it numerically, where ##j=\sqrt{-1}##. Is there any way to do that?

Thanks in advance

 

[Charles Link]

It isn't clear to me what ## E_1^m(z) ## is. Can you please write out this function in more detail.

 

[EngWiPy]

It isn't clear to me what ## E_1^m(z) ## is. Can you please write out this function in more detail.

It is

[tex]\left(\int_z^{\infty}\frac{e^{-t}}{t}\,dt\right)^m[/tex]