Results 231 to 240 of about 31,361 (268)
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The Annals of Mathematics, 1934
Verf. gibt eine eingehende Diskussion von vier besonderen Polynomklassen \(A,B,C,D\), die zueinander und zu den Klassen \(H\) und \(A_0\) der Hermiteschen bzw. Appellschen Polynome in folgender Beziehung stehen: \[ H\prec A\prec B\prec C;\quad A_0\prec B,\quad A_0\prec D. \] (\(H\prec A\) bedeutet, daß\ \(A\) eine Verallgemeinerung von \(H\) ist, usw.)
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Verf. gibt eine eingehende Diskussion von vier besonderen Polynomklassen \(A,B,C,D\), die zueinander und zu den Klassen \(H\) und \(A_0\) der Hermiteschen bzw. Appellschen Polynome in folgender Beziehung stehen: \[ H\prec A\prec B\prec C;\quad A_0\prec B,\quad A_0\prec D. \] (\(H\prec A\) bedeutet, daß\ \(A\) eine Verallgemeinerung von \(H\) ist, usw.)
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Polynomials and Complex Polynomials
1997If F is a field and n is a nonnegative integer, then a polynomial of degree n over F is a formal sum of the form $$P(x) = {a_0} + {a_1}x + \cdots + {a_n}{x^n}$$ With a i ∈ F for i = 0, .., n, a n ≠ 0 and x an indeterminate. A polynomial P(χ) over F is either a polynomial of some degree or the expression P(χ) = 0, which is called the zero ...
Benjamin Fine, Gerhard Rosenberger
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Journal of Mathematical Physics, 1970
The present work is concerned with what are called polynomial algebras as an extension of the work of Ramakrishnan and his colleagues on the algebras of matrices satisfying conditions like Lm = I and Lm = Lk. Assuming Lm to be an m-dimensional linear space, we generate a class of associative algebras called polynomial algebras by requiring that every ...
Raghavacharyulu, I. V. V. +1 more
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The present work is concerned with what are called polynomial algebras as an extension of the work of Ramakrishnan and his colleagues on the algebras of matrices satisfying conditions like Lm = I and Lm = Lk. Assuming Lm to be an m-dimensional linear space, we generate a class of associative algebras called polynomial algebras by requiring that every ...
Raghavacharyulu, I. V. V. +1 more
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On Polynomials in a Polynomial
Bulletin of the London Mathematical Society, 1972Evyatar, A., Scott, D. B.
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1966
Publisher Summary This chapter focuses on simple sets of orthogonal polynomials. These sets of polynomials arise in various ways, one of which is as the solutions of a class of differential equations. It has been shown that, under certain conditions, given any interval and a positive weight function on that interval, there exists a corresponding set ...
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Publisher Summary This chapter focuses on simple sets of orthogonal polynomials. These sets of polynomials arise in various ways, one of which is as the solutions of a class of differential equations. It has been shown that, under certain conditions, given any interval and a positive weight function on that interval, there exists a corresponding set ...
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Polynomials and Trigonometric Polynomials
1976Setting cos ϑ = x, the expressions $$ T_n \left( x \right) = \cos n\vartheta {\text{ }}U_n \left( x \right) = \frac{1} {{n + 1}}T'_{n + 1} \left( x \right) = \frac{{\sin \left( {n + 1} \right)\vartheta }} {{\sin \vartheta }}'{\text{ }}n = 0,1,2,...
George Pólya, Gabor Szegö
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Uncertain Polynomials. Interval Polynomials
1991Let the set U be the closed set of values s which are not located in a desired stability region Г, e.g., U is the closed right-half plane. The polynomial a( s, Q) is denoted U-stable if and only if no root of a(s, Q) is located in the undesired region, ie., $$a(s,Q) = \{ a(s,q){\rm{ : q}} \in Q\} \ne 0{\rm{ }}\forall s \in U$$ (21.1)
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Jensen polynomials for the Riemann zeta function and other sequences
Proceedings of the National Academy of Sciences of the United States of America, 2019Larry G Rolen
exaly