A review of branched continued fraction theory for the construction of multivariate rational approximations

While the history of continued fractions goes back to Euclid’s algorithm, branched continued fractions are only twenty years old. The idea to construct them was born in Lvov (U.S.S.R.) in the early sixties. The first and most general form of these fractions was introduced by Skorobogatko in [14] together with Droniuk, Bobyk and Ptashnik. An ordinary continued frution (CF) is an expression of the form &I + a1 Q2 , b, + b2+ b 3 +“’ . . .