Dear Mikola.

I don't think your expression can be evaluated in closed form.

You can write z= I/(2i+x) in trigonometric form z= re^(i a) and get representation using Euler formula: Re[ Li_2(z)] = Sum_{k=1}^{\infty}r^k cos(k a)/k^2

Dear Gro,

thank you for your answer.

That was my impression too from what I tried to do by myself.

On the other side, Lewin wrote at the beginning of Sec 5.3.1 that

"The following examples are due to Newman [8],

although similar formulas have been found by many other writers."

Do you, or somebody else, know that "writers" and their papers?

Best regards,

Mykola

Dear Mycola.  

I think you should look for a software named Wolfram Mathematica and use the function ''PolyLog''. See the help and you will find how to use it.

Thank you, Ailier,

although I always use Mahematica in my work, I found Maple preferable in dealing with functions of complex variables. Unfortunately, I did not find an answer in both of them.

Best,

Mykola