Book recommendation on infinite series and partial sums

[Angelcat]

I am wondering about any mathematics book (or PDF) on series which contains information regarding deriving partial sums of factorials, especially (or variations of):

[math]\sum_{n=1}^{k} n! = \frac{\text{Ei}(1)+E_{k+2}(-1)\Gamma(k+2)+\pi i-e}{e}[/math]
As a secondary priority it should be as complete and comprehensive as possible considering infinite series and partial sums in general as well.
The more suggestions the merrier, thank you in advance!

Regards,
Angelcat.

 

[pka]

A good Calculus textbook is helpful. Here is a free one for downloading:
In Elementary Calculus: An Infinitesimal Approach. The chapters and whole book is a free down-load at HERE
There many texts in any college library. Look for INFINITE SERIES by James M. Hyslop.

 

[Angelcat]

A good Calculus textbook is helpful. Here is a free one for downloading:
In Elementary Calculus: An Infinitesimal Approach. The chapters and whole book is a free down-load at HERE
There many texts in any college library. Look for INFINITE SERIES by James M. Hyslop.

Does the Hyslop book contain the derivation of the partial sum stated above? That is the one I am looking for. I could not find it in the online book but maybe I missed it; could you in that case refer to the correct page? I have also tried the references in https://mathworld.wolfram.com/FactorialSums.html but I could not find it in those either I would be very grateful if I found a derivation of specifically that partial sum.