Each entry of these previously known determinant formulas is given as a finite linear combination of elementary/ complete symmetric polynomials
, while in our formula it is given as a possibly infinite linear combination of Grothendieck polynomials
associated to one row partitions.
Gautschi collects exercises and solutions from his textbook on orthogonal polynomials
in MATLAB, edits them slightly to make them self-contained, and adds many new ones.
A generalisation of synthetic division and a general theorem of division of polynomials
A class of polynomials
f(x) suiting our demands is introduced, and we showed their existence by numerical experiments.
The problem of stability of systems can be supposed as the problem of stability of their characteristic polynomials
The problem of division was reduced by using zeros of polynomials
to find inverse of a number modulo prime powers.
Tutte in 1954 in  as a generalization of chromatic polynomials
studied by Birkhoff  and Whitney .
A method to determine in an efficient way the Laurent polynomials
of Hermite interpolation is presented in .
Fomin and Green gave a version for certain non-commutative symmetric functions, which led to combinatorial formulas for characters of representations associated to stable Schubert and stable Grothendieck polynomials
Keywords: legendre associated functions, Legendre polynomials
, recurrence relations, stability.
n and each coefficient's commitment of added sum of polynomials
of f(x) and k(x) as follows: ([s.
Let C [x, y, z] be the ring of polynomials
in the variables x, y, z with coefficients in C.
or ultraspherical polynomials
This can be done for the unispherical windows  based on Gegenbauer polynomials
as well as for windows proposed by Zierhofer .
The more classical examples of linear positive operators throughout approximation process are the Bernstein polynomials
, which are defined by Bernstein  as following: