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Codimensions of generalized polynomial identities

Sbornik: Mathematics, 2010
Let $A$ be a finite-dimensional associative algebra over a field of characteristic $0$. Then there exist $C \in \mathbb Q_+$, $t, d \in \mathbb Z_+$ such that $gc_n(A) \sim C n^t d^n$ as $n \to \infty$ and $d$ proves to coincide with $PI\exp(A)$.
Aleksei S Gordienko
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Regev’s and Amitsur’s conjectures for codimensions of generalized polynomial identities

Journal of Mathematical Sciences, 2009
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A Note on Generalized Polynomial Identities

Canadian Mathematical Bulletin, 1972
Let A be an algebra with 1 over a field F and let B be a fixed F-basis of A. Let F〈x〉=F〈x1,…, xn,…,〉 be the free algebra over F in noncommutative indeterminates x1,…, xn,…, and denote by AF〈x〉 the free product of A and F〈x〉 over F. The elements of AF〈x〉 of the form varies, repetitions allowed) form an F-basis of AF〈x〉.
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Identities with Generalized Derivations and Multilinear Polynomials

Bulletin of the Iranian Mathematical Society, 2019
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On Some Generalized Identities with Derivations on Multilinear Polynomials

Algebra Colloquium, 2010
Let K be a commutative ring with unity, R a prime K-algebra of characteristic different from 2, Z(R) the center of R, f(x1,…,xn) a non-central multilinear polynomial over K, d and δ derivations of R, a and b fixed elements of R. Denote by f(R) the set of all evaluations of the polynomial f(x1,…,xn) in R. If a[d(u),u] + [δ (u),u]b = 0 for any u ∈ f(R),
CARINI, Luisa, DE FILIPPIS, Vincenzo, O. M. Di Vincenzo   +2 more
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Multivariate generalized Bernstein polynomials: identities for orthogonal polynomials of two variables

Numerical Algorithms, 2008
The authors define polynomials \(B_\mathbf{k}^n(\mathbf{x}; \omega | q)\), which they call multivariate generalized Bernstein polynomials, depending on the two parameters \(q\) and \(\omega\). These polynomials inherit many special cases and identities can be retrieved from limit forms.
Stanislaw Lewanowicz, Pawel Wozny, Iván Area, Eduardo Godoy   +3 more
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Some identities for generalized Chebyshev polynomials

2019 Days on Diffraction (DD), 2019
We consider special linear combinations of classical Chebyshev polynomials (of the 2nd kind) generating a class of polynomials related to “local perturbations” of the coefficients of the discrete Schrodinger equation. These polynomials are called the generalized Chebyshev polynomials.
V.V. Borzov, E.V. Damaskinsky
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Identities involving generalized Fibonacci-type polynomials

Applied Mathematics and Computation, 2011
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Binomial Identities Involving The Generalized Fibonacci Type Polynomials.

Ars Comb., 2011
We present some binomial identities for sums of the bivariate Fibonacci polynomials and for weighted sums of the usual Fibonacci polynomials with indices in arithmetic progression.
Kilic, Emrah, Irmak, Nurettin
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Identities and generating functions on Chebyshev polynomials

Georgian Mathematical Journal, 2012
Summary: We present the classical theory of Chebyshev polynomials starting from the definition of a family of complex polynomials, including both the first and second kind classical Chebyshev polynomials, which are related to their real and imaginary parts.
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