EuDML | Browse

Displaying 21 – 32 of 32

Connections between Romanovski and other polynomials

Hans Weber (2007)

Open Mathematics

A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrödinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.

Consistency of trigonometric and polynomial regression estimators

Waldemar Popiński (1998)

Applicationes Mathematicae

The problem of nonparametric regression function estimation is considered using the complete orthonormal system of trigonometric functions or Legendre polynomials $e_{k}$ , k=0,1,..., for the observation model $y_{i} = f (x_{i}) + η_{i}$ , i=1,...,n, where the $η_{i}$ are independent random variables with zero mean value and finite variance, and the observation points $x_{i} \in [a, b]$ , i=1,...,n, form a random sample from a distribution with density $ϱ \in L^{1} [a, b]$ . Sufficient and necessary conditions are obtained for consistency in the sense of the errors $∥ f - {\hat{f}}_{N} ∥, | f (x) -_{N} (x) |$ , $x \in [a, b]$ ,...

Displaying 21 – 32 of 32

Connections between Romanovski and other polynomials

Consistency of trigonometric and polynomial regression estimators

Construction of a recurrence relation of the lowest order for coefficients of the Gegenbauer series

Construction of the lowest-order recurrence relation for the Jacobi coefficients

Continuité et différentiabilité des translations dans un espace Gaussien.

Continuous symmetrized Sobolev inner products of order $N$ . II.

Contributions to the theory of Hermitian series. III: Mean values.

Convergence of Padé approximants for a q-hypergeometric series (Wynn's Power Series III).

Convergence of Padé approximants for a q-hypergeometric series (Wynn's Power Series III). (Summary).

Convergence of Padé approximants for a q-hypergeometric series (Wynn's Power Series I). (Summary).

Convergence of Padé approximations for a q-hypergeometric series (Wynn's Power Series I).

Creation and annihilation operators for orthogonal polynomials of continuous and discrete variables.

Currently displaying 21 – 32 of 32