How to implement the given series in WL?

Questions
1

Hi
I’m trying to implement the series in Mathematica, but somehow it is not producing the required results.
Could you please help me out?

zainsb1.png
zainsb1.png391×170 9.05 KB

This is the series, and i’m implementing it like:

For[i = 0, i <= 2, i++,
 Print[D[
\!\(\*UnderscriptBox[
OverscriptBox[\(\[Sum]\), \(k + 1\)], \(k = i\)]\)Subscript[a, 
     k] (D[s[\[Xi]], \[Xi]]/s[\[Xi]])^k],
  Print[];]]

I have added the source file as well, zain.nb

Regards

2

How about

Sum[Subscript[a, k] (D[s[\[Xi]], \[Xi]]/s[\[Xi]])^k, {k, 0, 2}]

You write a derivative D symbol that has no match in the formula you are trying to implement.

Two-dimensional traditional notations for sums and integrals are tricky. I use them only for final display, not for calculations.