Search results for "Gegenbauer polynomials"
showing 6 items of 6 documents
Polynomials generated by linear operators
2004
We study the class of Banach algebra-valued n n -homogeneous polynomials generated by the n t h n^{th} powers of linear operators. We compare it with the finite type polynomials. We introduce a topology w E F w_{EF} on E , E, similar to the weak topology, to clarify the features of these polynomials.
Complex Numbers and Polynomials
2016
As mentioned in Chap. 1, for a given set and an operator applied to its elements, if the result of the operation is still an element of the set regardless of the input of the operator, then the set is said closed with respect to that operator.
On the zeros of Jacobi polynomials
1994
Indefinite integrals for some orthogonal polynomials obtained using integrating factors
2020
A method has been presented recently for deriving integrals of special functions using two kinds of integrating factor for the homogeneous second-order linear differential equations which many spec...
Upper bounds for the zeros of ultraspherical polynomials
1990
AbstractFor k = 1, 2, …, [n2] let xnk(λ) denote the Kth positive zero in decreasing order of the ultraspherical polynomial Pn(λ)(x). We establish upper bounds for xnk(λ). All the bounds become exact when λ = 0 and, in some cases (see case (iii) of Theorem 3.1), also when λ = 1. As a consequence of our results, we obtain for the largest zero xn1(λ)0.. We point out that our results remain useful for large values of λ. Numerical examples show that our upper bounds are quite sharp.