Results 161 to 170 of about 601,525 (187)

Finite Differences and Orthogonal Polynomials

The Ramanujan Journal, 1999
By combining finite differences with symmetric functions, we present an elementary demonstration for the limit relation from Laguerre to Hermite polynomials, proposed by Richard Askey. Another limit relation between these two polynomials is also established.
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Characterization of polynomials and divided difference

Proceedings of the Indian Academy of Sciences - Section A, 1995
The authors offer two additional proofs of a result by \textit{J. Schwaiger} [Aequationes Math. 48, No. 2-3, 317-323 (1994; Zbl 0810.39007)] that the \((n-1)\)-st divided difference (with variable spans) of \(f\) is a function of the sum of its \(n\) variables iff \(f\) is a polynomial of degree at most \(n\); and \(g\) is linear.
Prasanna K. Sahoo, Pl. Kannappan
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An Existence Theorem for Difference Polynomials

Proceedings of the American Mathematical Society, 1966
Introduction. The abstract varieties (also called manifolds) of difference algebra [2], [3] have not heretofore had a realization as sets of functions comparable to the realization provided for differential manifolds by the analytic existence theorem for differential equations (see [4], particularly p. 23).
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On the difference of successive Gaussian polynomials

Journal of Statistical Planning and Inference, 1993
Let \(M,N\in\mathbb{Z}\); as usual, define the ``Gaussian polynomials'' by \({N\brack M}=\prod^ M_ 1(1-q^{N+1-j})\) \((1-q^ j)^{-1}\), if \(0\leq M\leq N\). Otherwise, put \({N\brack M}=0\). According to the author's introduction, ``the object in this paper is to relate differences of Gaussian polynomials to partitions through the use of Frobenius ...
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Singular Manifolds of Difference Polynomials

The Annals of Mathematics, 1951
1. Let F be an algebraically irreducible difference polynomial in unknowns Y1, Y2, ... , yn with coefficients in a difference field W. We showed previously' that the irreducible components of the manifold of F are of two types: ordinary manifolds not held by any polynomial of lower effective order than F in any yj; and essential singular manifolds ...
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Conversion of Polynomials between Different Polynomial Bases [PDF]

IMA Journal of Numerical Analysis, 1981
Y. L. Luke, B. Y. Ting
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Nanofluidics for osmotic energy conversion

Nature Reviews Materials, 2021
Zhen Zhang, Liping Wen, Lei Jiang
exaly  

The fundamentals and applications of ferroelectric HfO2

Nature Reviews Materials, 2022
Uwe Schroeder, Min Hyuk Park, Thomas Mikolajick   +2 more
exaly  

Characteristics of SARS-CoV-2 and COVID-19

Nature Reviews Microbiology, 2020
Ben Hu, Hua Guo, Peng Zhou
exaly  

Difference-in-Differences with multiple time periods

Journal of Econometrics, 2021
Brantly Callaway
exaly