Some recurrence relations among the radial matrix elements for the relativistic hydrogenic atoms

The general calculation formula for the matrix elements is derived. We present a very lengthy and complicated general recurrence relation among the matrix elements of rk. Some useful recurrence relations among the matrix elements are studied in some special cases, which include the matrix elements of rk calculated in the same state vertical bar n'l'>, the different states vertical bar n'l1'> and vertical bar n'l2'>, the k= vertical bar l1-l2 vertical bar and k=l1+l2+1. On the basis of the integral properties of the product of two associated Laguerre polynomials multiplied by a weight factor, we obtain a new recurrence relation between the matrix elements and . Another recurrence relation involving the matrix elements of logarithmic functions ln(2r/α'n') (α'=a0mc2/ZEn') is investigated