Newmark scheme beta and gamma parameters

Hi,
Concerning the Newmark method with central difference for an explicit resolution I want to know where the parameters beta and gamma come from ?

I have found this :

http://www.stanford.edu/group/frg/course_work/AA242B/CA-AA242B-Ch7.pdf
but how do these parameters appear ?

Using RADIOSS, the theory manual says the remainder of the taylor's series is computed using numerical integration but I don't know which rule is used.

Some explanation needed and appreciated.

Thanks.