Author

# M. K. Kerimov

Bio: M. K. Kerimov is an academic researcher from Russian Academy of Sciences. The author has contributed to research in topics: Bessel function & Series (mathematics). The author has an hindex of 7, co-authored 70 publications receiving 137 citations.

##### Papers

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TL;DR: A detailed overview of the results concerning the real zeros of the Bessel functions of the first and second kinds and general cylinder functions can be found in this article, where the main emphasis is placed on classical results, which are still important.

Abstract: The zeros of Bessel functions play an important role in computational mathematics, mathematical physics, and other areas of natural sciences. Studies addressing these zeros (their properties, computational methods) can be found in various sources. This paper offers a detailed overview of the results concerning the real zeros of the Bessel functions of the first and second kinds and general cylinder functions. The author intends to publish several overviews on this subject. In this first publication, works dealing with real zeros are analyzed. Primary emphasis is placed on classical results, which are still important. Some of the most recent publications are also discussed.

19 citations

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TL;DR: Two useful estimates for the Fourier transform in the space of square integrable functions on certain classes of functions characterized by the generalized continuity modulus have been proved in this article, where they are used to obtain a generalized continuity matrix.

Abstract: Two useful estimates are proved for the Fourier transform in the space of square integrable functions on certain classes of functions characterized by the generalized continuity modulus.

18 citations

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TL;DR: In this article, a detailed overview of the results concerning the theory and applications of the Rayleigh special function starting from its appearance in science until recent years is provided, and an extensive bibliography is presented.

Abstract: The author’s previous work provided a detailed overview of the results concerning the theory and applications of the Rayleigh special function starting from its appearance in science until recent years. Its numerous applications in various areas of mathematics, physics, and other fields were described, and an extensive bibliography was presented. This work overviews the studies not covered in the previous one and addresses new results published in many monographs and journals. Additionally, results concerning the estimation of zeros of some special polynomials and functions closely related to the Rayleigh function are described. The overview embraces the issues addressed in the scientific literature up to the last years.

15 citations

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TL;DR: In this article, the generalized modulus of continuity (GOML) is used to estimate the best approximation of a function characterized by the generalized Fourier-Bessel series.

Abstract: Some issues concerning the approximation of one-variable functions from the class $\mathbb{L}_2 $ by nth-order partial sums of Fourier-Bessel series are studied. Several theorems are proved that estimate the best approximation of a function characterized by the generalized modulus of continuity.

13 citations

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TL;DR: In this paper, the Fourier-Bessel integral transform in L 2 (ℝ+) was shown to have a generalized modulus of continuity, and two estimates useful in applications were proved.

Abstract: Two estimates useful in applications are proved for the Fourier-Bessel integral transform in L2(ℝ+) as applied to some classes of functions characterized by a generalized modulus of continuity.

11 citations

##### Cited by

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01 Jan 2016

TL;DR: The table of integrals series and products is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.

Abstract: Thank you very much for downloading table of integrals series and products. Maybe you have knowledge that, people have look hundreds times for their chosen books like this table of integrals series and products, but end up in harmful downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they cope with some harmful virus inside their laptop. table of integrals series and products is available in our book collection an online access to it is set as public so you can get it instantly. Our book servers saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the table of integrals series and products is universally compatible with any devices to read.

4,085 citations

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1,969 citations

01 Jan 2007

TL;DR: Two algorithms for generating the Gaussian quadrature rule defined by the weight function when: a) the three term recurrence relation is known for the orthogonal polynomials generated by $\omega$(t), and b) the moments of the weightfunction are known or can be calculated.

Abstract: Most numerical integration techniques consist of approximating the integrand by a polynomial in a region or regions and then integrating the polynomial exactly. Often a complicated integrand can be factored into a non-negative ''weight'' function and another function better approximated by a polynomial, thus $\int_{a}^{b} g(t)dt = \int_{a}^{b} \omega (t)f(t)dt \approx \sum_{i=1}^{N} w_i f(t_i)$. Hopefully, the quadrature rule ${\{w_j, t_j\}}_{j=1}^{N}$ corresponding to the weight function $\omega$(t) is available in tabulated form, but more likely it is not. We present here two algorithms for generating the Gaussian quadrature rule defined by the weight function when: a) the three term recurrence relation is known for the orthogonal polynomials generated by $\omega$(t), and b) the moments of the weight function are known or can be calculated.

1,007 citations

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42 citations

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TL;DR: Following theory and simulations, it is proposed to modify – directly and solely – the noise variance estimate, and investigate this solution on real imaging data from a range of modalities.

37 citations