Results 21 to 30 of about 56,399 (238)

Polynomials of binomial type and Lucas’ Theorem [PDF]

Proceedings of the American Mathematical Society, 2015
At the intersection of number theory, commutative algebra and combinatorics. The new version has additional references.
David Goss
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Polynomials of binomial type and approximation theory

Journal of Approximation Theory, 1978
AbstractWe study exponential operators Sλ(ƒ, t) satisfying for t ϵ (A, B) with A − ∞, p(A) = 0, p′(A) ≠ 0. We normalize these operators by A = 0, p(A) = 0, p′(A) = 1. We show that there is a one-to-one correspondence between these operators and basic sets of binomial type {Pn(x)}n = 0∞ with Pn(x) ⩾ 0 for x 0.
Mourad E. H. Ismail
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Linear Approximation Processes Based on Binomial Polynomials

Mathematics
The purpose of the article is to highlight the role of binomial polynomials in the construction of classes of positive linear approximation sequences on Banach spaces.
Octavian Agratini, Maria Crăciun
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Shifted jack polynomials, binomial formula, and applications [PDF]

Mathematical Research Letters, 1997
AMS TeX, 8 pages.
Andreĭ Okounkov, Grigori Olshanski
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Polynomial Identities for Binomial Sums of Harmonic Numbers of Higher Order

Mathematics
We study the formulas for binomial sums of harmonic numbers of higher order ∑k=0nHk(r)nk(1−q)kqn−k=Hn(r)−∑j=1nDr(n,j)qjj. Recently, Mneimneh proved that D1(n,j)=1. In this paper, we find several different expressions of Dr(n,j) for r≥1.
Takao Komatsu, B. Sury
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Binomial-Weighted Orthogonal Polynomials [PDF]

Journal of the ACM, 1967
This paper discusses a set of polynomials, {φ r ( s )}, orthogonal over a discrete range, with binomial distribution, b ( s ; n , p ), as the weighting function.
Tzay Y. Young
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REPRESENTATION OF SOME BINOMIAL COEFFICIENTS BY POLYNOMIALS [PDF]

Bulletin of the Korean Mathematical Society, 2007
The unique positive zero of Fm(z) := z2m− zm+1− zm−1− 1 leads to analogues of 2 (2n k ) (k even) by using hypergeometric functions. The minimal polynomials of these analogues are related to Chebyshev polynomials, and the minimal polynomial of an analogue of 2 (2n k ) (k even > 2) can be computed by using an analogue of 2 (2n 2 ) . In this paper we show
Seon-Hong Kim
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Polynomials of binomial type and compound Poisson processes

Journal of Mathematical Analysis and Applications, 1988
The theory of polynomials of binomial type, i.e. of polynomials \((q_ n)_ 0\) satisfying \(q_ n(x+y)=\sum^{n}_{k=0}\left( \begin{matrix} n\\ k\end{matrix} \right)q_ k(x)q_{n-k}(y)\), was developed by \textit{G.-C. Rota}, \textit{D. Kahaner} and \textit{A. Odlyzko} [cf. J. Math. Anal. Appl. 42, 684-760 (1973; Zbl 0267.05004)].
A. J. Stam
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Integer-valued polynomials and binomially Noetherian rings

Zanco Journal of Pure and Applied Sciences, 2022
for each and i ≥ 0. The polynomial ring of integer-valued in rational polynomial is defined by Int ( an important example for binomial ring and is non-Noetherian ring. In this paper the algebraic structure of binomial rings has been studied by their
Shadman Kareem
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Polynomials satisfying a binomial theorem

Journal of Mathematical Analysis and Applications, 1970
B. C. Carlson
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