Riordan matrices in the reciprocation of quadratic polynomials
The paper deals with two arithmetical triangles: The first are remainders that appear in an iterative process while the second can be interpreted as change of variables. All elements in both type are invertible Riordan arrays (Riordan matrices). In Section 2, the authors develop the theory used in the following sections. In Section 3, the authors compare the remainder of a Taylor expansion with an element of the Riordan group. Finally, they get the Pascal triangle as product of certain matrices. All their remainders are 7-matrices (see (5) from References). In Section 4 the change of variables obtained in Section 3 is studied. In Section 5 some known formulas of the sums of powers of natural numbers are recovered.
scientific article; zbMATH DE number 5549279
scientific article