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Due to the fact that in the case $q > 1$ the $q$ -Bernstein polynomials are no longer positive linear operators on $C [0, 1],$ the study of their convergence properties turns out to be essentially more difficult than that for $q < 1 .$ In this paper, new saturation theorems related to the convergence of $q$ -Bernstein polynomials in the case $q > 1$ are proved.

The special function ش

Andrea Ossicini (2005)

Kragujevac Journal of Mathematics

The special function ش , II

Andrea Ossicini (2006)

Kragujevac Journal of Mathematics

The special function ش , III

Andrea Ossicini (2008)

Kragujevac Journal of Mathematics

The Spectrum of Hill's Equation.

P. van Moerbeke, H.P. McKean (1975)

Inventiones mathematicae

The spt-crank for overpartitions

Frank G. Garvan, Chris Jennings-Shaffer (2014)

Acta Arithmetica

Bringmann, Lovejoy, and Osburn (2009, 2010) showed that the generating functions of the spt-overpartition functions $\bar{s p t} (n)$ , ${\bar{s p t}}_{1} (n)$ , ${\bar{s p t}}_{2} (n)$ , and M2spt(n) are quasimock theta functions, and satisfy a number of simple Ramanujan-like congruences. Andrews, Garvan, and Liang (2012) defined an spt-crank in terms of weighted vector partitions which combinatorially explain simple congruences modulo 5 and 7 for spt(n). Chen, Ji, and Zang (2013) were able to define this spt-crank in terms of ordinary partitions. In this...

The structure of totally disconnected, locally compact groups.

G. Willis (1994)

Mathematische Annalen

The summation package Sigma: underlying principles and a rhombus tiling application.

Schneider, Carsten (2004)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

The symmetrical $H_{q}$ -semiclassical orthogonal polynomials of class one.

Ghressi, Abdallah, Khériji, Lotfi (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

The $(t, q)$ -analogs of secant and tangent numbers.

Foata, Dominique, Han, Guo-Niu (2011)

The Electronic Journal of Combinatorics [electronic only]

The tangent function and power residues modulo primes

Zhi-Wei Sun (2023)

Czechoslovak Mathematical Journal

Let $p$ be an odd prime, and let $a$ be an integer not divisible by $p$ . When $m$ is a positive integer with $p \equiv 1 (mod 2 m)$ and $2$ is an $m$ th power residue modulo $p$ , we determine the value of the product $\prod_{k \in R_{m} (p)} (1 + tan (π a k / p))$ , where $R_{m} (p) = {0 < k < p : k \in ℤ is an m th power residue modulo p} .$ In particular, if $p = x^{2} + 64 y^{2}$ with $x, y \in ℤ$ , then $\prod_{k \in R_{4} (p)} (1 + tan π \frac{a k}{p}) = {(- 1)}^{y} {(- 2)}^{(p - 1) / 8} .$

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The relationship between Zhedanov's algebra $A W (3)$ and the double affine Hecke algebra in the rank one case.

The representation and the approximation of one class of exponential functions

The restricted Toda chain, exponential Riordan arrays, and Hankel transforms.

The roots of the third J. Jckson $q$ -Bessel function.

The second-order Klein-Gordon field equation.

The second-order self-associated orthogonal sequences.

The sharpness of convergence results for $q$ -Bernstein polynomials in the case $q > 1$

The special function ش

The special function ش , II

The special function ش , III

The Spectrum of Hill's Equation.

The spt-crank for overpartitions

The structure of totally disconnected, locally compact groups.

The summation package Sigma: underlying principles and a rhombus tiling application.

The symmetrical $H_{q}$ -semiclassical orthogonal polynomials of class one.

The $(t, q)$ -analogs of secant and tangent numbers.

The tangent function and power residues modulo primes

The transcendence of certain quasi-periods associated with abelian functions in two variables

The triplication formula for Gauss sums.

The truncated exponential polynomials, the associated Hermite forms and applications.

Currently displaying 1761 – 1780 of 2026