I SENT THIS TO BURINSKII, NO COMMENTS, FOR THE HELL OF IT.
MUCH AS HE MIGHT LIKE TO, BURINSKII CANNOT DISMISS MY MATHEMATICS.
When we integrate by ‘r’, we need to analyze near the inner limit, where still in the DKS mode, the radius is <<1, or here, 1/137. Here I play my “quick and dirty” game because it is OK. Inside the brackets, IN THIS NEAR-FIELD we have effectively, 1 + 1/r(π/2) . THIS IS MY GAME, MATES. There is another factor of 1/2 from the start, as this form was reduced a bit.