On the real quadratic fields with certain continued fraction expansions and fundamental units

The purpose of this paper is to investigate the real quadratic number fields q(√d ) which contain the specific form of the continued fractions expansions of integral basis element where d≡2,3(mod4) is a square free positive integer. besides, the present paper deals with determining the fundamental unit ϵd=(td+ud√d )/ 2⟩1 and nd and md yokoi's d-invariants by reference to continued fraction expansion of integral basis element where ℓ(d) is a period length. moreover, we mention class number for such fields. also, we give some numerical results concluded in the tables.