A continued fraction of a inhomogeneous linear form
Let α,β be real numbers 0≤α<1,0≤β<1. They define at the plane (y,z)∈R2 the inhomogeneous linear form Lα,β(y,z)=-β+αy+z. We propose the algorithm of an expansion of this linear form into the 'inhomogeneous continued fraction' Lα,β~[0;b1,b2,...]mod[0;a1,a2,...]. Inhomogeneous continued fraction generalize the classic regular continued fraction: for β=0 every bn=0 and we get the continued fraction expansion of the number α: Lα,0~mod[0;a1,a2,...]. Some properties of inhomogeneous continued fractions are proved.
continued fractions, inhomogeneous Diophantine approximations, Euclid algorithm
Mathematical modelling in actual problems of science and technics