Berlekamp–Massey Algorithm, Continued Fractions, Padé Approximations, and Orthogonal Polynomials

The Berlekamp–Massey algorithm (further, the BMA) is interpreted as an algorithm for constructing Padé approximations to the Laurent series over an arbitrary field with singularity at infinity. It is shown that the BMA is an iterative procedure for constructing the sequence of polynomials orthogonal to the corresponding space of polynomials with respect to the inner product determined by the given series. The BMA is used to expand the exponential in continued fractions and calculate its Pade approximations.