Results 31 to 40 of about 4,735 (303)
Identity-Type Functions and Polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2007 For a noncommuting product of functions, similar to convolutions, an “identity-type function” leaving a specific function invariant is defined. It is evaluated for any choice of function on which it acts by solving a functional equation. A closed-form representation for the identity-type function of(1+t)−b(b>0)is obtained, which is a solution of a ...
M. Aslam Chaudhry, Asghar Qadir
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The Polarization Theorem and Polynomial Identities for Matrix Functions
Известия Иркутского государственного университета: Серия "Математика", 2017 In this article the simple combinatorial proof of the known polarization theorem (about the restoration of a polyadditive symmetric function over its values on a diagonal) is given.
G.P. Egorychev
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Quasi-Polynomials of Capelli. II [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2020 This paper observes the continuation of the study of a certain kind of polynomials of type Capelli (Capelli quasi-polynomials) belonging to the free associative algebra F{X S Y } considered over an arbitrary field F and generated by two disjoint ...
Stepan Yuryevich Antonov +1 more
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Irreducible polynomial identities in anticommutative algebras [PDF]
, 1970 The methods introduced by J. M. Osborn for isolating those polynomial identities worth studying in commutative algebras are here modified to yield three theorems for anticommutative algebras.
Seymour Kass, William G. Witthoft
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Mathematics, 2022 Numerous polynomial variations and their extensions have been explored extensively and found applications in a variety of research fields. The purpose of this research is to establish a unified class of Apostol–Genocchi polynomials based on poly-Daehee ...
Talha Usman +5 more
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Identities of bilinear mappings and graded polynomial identities of matrices [PDF]
, 2003 We describe the polynomial identities of the bilinear mappings V⊗W→K and Vr⊗Vr∗→Mr(K), where V, W, Vr are finite dimensional vector spaces over a field K of characteristic 0, dimVr=r and Mr(K) is the r×r matrix algebra.
Drensky, V., Bahturin, Yu.A.
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Attaching a matrix algebra to affine group schemes: Polynomial identities [PDF]
, 2023 We give a definition of polynomial identities for affine group schemes; over a field F of characteristic 0, the identities of an affine group scheme turn out to coincide with the identities of a certain matrix algebra over F.
Lucio Centrone
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Derivation of Identities Involving Bernoulli and Euler Numbers
International Journal of Mathematics and Mathematical Sciences, 2012 We derive some new and interesting identities involving Bernoulli and Euler numbers by using some polynomial identities and p-adic integrals on ℤ𝑝.
Imju Lee, Dae San Kim
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Congruences from $q$-Catalan Identities [PDF]
Transactions on Combinatorics, 2016 In this paper, by studying three $q$-Catalan identities given by Andrews, we arrive at a certain number of congruences. These congruences are all modulo $Phi_n(q)$, the $n$-th cyclotomic polynomial or the related functions and modulo $q$-integers
Qing Zou
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Polynomial identities on eigenforms
Journal of Number Theory, 2016 In this paper, we fix a polynomial with complex coefficients and determine the eigenforms for SL2(Z) which can be expressed as the fixed polynomial evaluated at other eigenforms. In particular, we show that when one excludes trivial cases, only finitely many such identities hold for a fixed polynomial.
Richey, Joseph, Shutty, Noah
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