Results 171 to 180 of about 696 (218)

Analysis of mean-field models arising from self-attention dynamics in transformer architectures with layer normalization. [PDF]

Philos Trans A Math Phys Eng Sci
Burger M, Kabri S, Korolev Y, Roith T, Weigand L.   +4 more
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Series of products of Gegenbauer polynomials

Mathematische Zeitschrift, 1955
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Derivatives of Generalized Gegenbauer Polynomials

Theoretical and Mathematical Physics, 2002
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García Fuertes, W., Perelomov, A. M.
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Gegenbauer Polynomials Revisited

The Fibonacci Quarterly, 1985
Der Gegenstand dieser Arbeit sind spezielle Polynome, die sich in der Tafel der Gegenbauerschen Polynome entlang der abnehmenden Diagonalen bilden. Dabei werden einige Eigenschaften dieser Polynome diskutiert wie z.B. expliziter Ausdruck, erzeugende Funktion, rekurrenter Ausdruck, Differentialgleichung u.s.w.
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Information entropy of Gegenbauer polynomials

Journal of Physics A: Mathematical and General, 2000
Summary: The information entropy of Gegenbauer polynomials is relevant since this is related to the angular part of the information entropies of certain quantum mechanical systems such as the harmonic oscillator and the hydrogen atom in \(D\) dimensions.
Buyarov, V. S., López-Artés, P., Martínez-Finkelshtein, A., Van Assche, W.   +3 more
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Appendix: Gegenbauer Polynomials

2016
This chapter collects some properties of the Gegenbauer polynomials that we use throughout this work, in particular, in the proof of the explicit formulae for differential symmetry breaking operators (Theorems 1.5, 1.6, 1.7, and 1.8) and the factorization identities for special parameters (Theorems 13.1, 13.2, and 13.3).
Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner   +2 more
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Higher Spin Generalisation of the Gegenbauer Polynomials

Complex Analysis and Operator Theory, 2016
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David Eelbode, Tim Janssens
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Gegenbauer-Sobolev Orthogonal Polynomials

1994
In this paper, orthogonal polynomials in the Sobolev space W 1,2([-1,1], p (α),λ p (α)), where \({\rho ^{(\alpha )}} = {(1 - {x^2})^{\alpha - \frac{1}{2}}},\alpha >- \frac{1}{2}\) and λ ≥ 0, are studied. For these non-standard orthogonal polynomials algebraic and differential properties are obtained, as well as the relation with the classical ...
Francisco Marcellán, Teresa E. Pérez, Miguel A. Piñar   +2 more
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Gegenbauer, Jacobi, and Orthogonal Polynomials

2016
In earlier chapters we dealt with special sets of orthogonal polynomials, namely, Chebyshev and Hermite polynomials. In Chs. 9 and 10 we will study other orthogonal polynomials, namely, Laguerre and Legendre. All of these polynomial functions share many properties.
Vasudevan Lakshminarayanan, L. Srinivasa Varadharajan   +1 more
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Uniform inequalities for Gegenbauer polynomials

Acta Mathematica Hungarica, 1996
The usual asymptotic representations of the Gegenbauer (ultraspherical) polynomials do not yield bounds on their absolute values which hold equally on the interval \(-1\leq x\leq 1\). But in the Legendre case (index \(\lambda= {1\over 2}\)) and more generally in the case of \(0\leq \lambda\leq 1\) such estimates exist.
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