共查询到20条相似文献,搜索用时 15 毫秒
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We establish lower and upper bounds for the Bessel functionJ v (x) and the modified Bessel functionI v(x) of the first kind. Our chief tool is the differential equation satisfied by these functions. 相似文献
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In this paper, our aim is to show some mean value inequalities for the modified Bessel functions of the first and second kind. Our proofs are based on some bounds for the logarithmic derivatives of these functions, which are in fact equivalent to the corresponding Turán-type inequalities for these functions. As an application of the results concerning the modified Bessel function of the second kind, we prove that the cumulative distribution function of the gamma–gamma distribution is log-concave. At the end of this paper, several open problems are posed, which may be of interest for further research. 相似文献
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Let jvk, yvk and cvk denote the kth positive zeros of the Bessel functions Jv(x), Yv(x) and of the general cylinder function Cv(x) = cos αJv(x)?sin αYv(x), 0 ? α < π, respectively. In this paper we extend to cvk, k = 2, 3,..., some linear inequalities presently known only for jvk. In the case of the zeros yvk we are able to extend these inequalities also to k = 1. Finally in the case of the first positive zero jv1 we compare the linear enequalities given in [9] with some other known inequalities. 相似文献
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D. Babusci G. Dattoli B. Germano M.R. Martinelli P.E. Ricci 《Applied Mathematics Letters》2013,26(3):351-354
We use the operator method to evaluate a class of integrals involving Bessel or Bessel-type functions. The technique that we propose is based on the formal reduction of functions in this family to Gaussians. 相似文献
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Jesús García-Ravelo Axel Schulze-Halberg José Juan Peña Gil Alfonso Queijeiro 《Applied Mathematics Letters》2010,23(4):462-465
We construct ladder operators for spherical Bessel functions of arbitrary order. Our ladder operators act independently on two parameters, one of which is the order of the spherical Bessel function, while the other parameter is a multiplicative factor in the spherical Bessel function’s argument. 相似文献
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In this paper our aim is to show some new inequalities of the Redheffer type for Bessel and modified Bessel functions of the first kind. The key tools in our proofs are some classical results on the monotonicity of quotients of differentiable functions as well as on the monotonicity of quotients of two power series. We also use some known results on the quotients of Bessel and modified Bessel functions of the first kind, and by using the monotonicity of the Dirichlet eta function we prove a sharp inequality for the tangent function. At the end of the paper a conjecture is stated, which may be of interest for further research. 相似文献
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M.E Cohen 《Journal of Mathematical Analysis and Applications》1977,57(2):469-475
In this paper, the product of a Jacobi polynomial and function is shown to generate the Jacobi polynomial. This type of expansion was previously known for all the classical orthogonal polynomials except the Jacobi. The result is then used to obtain generalizations to Watson's [10] multiplication theorem involving integrals of Bessel functions. The integrals considered are of the form ∝∞0t1?λJv(tx1) Jμ(tx2) Jσ(tx3) Jτ(tx4) dt. 相似文献
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Árpád Baricz Dragana Jankov Maširević Tibor K. Pogány Róbert Szász 《Journal of Mathematical Analysis and Applications》2015
In this paper our aim is to present an elementary proof of an identity of Calogero concerning the zeros of Bessel functions of the first kind. Moreover, by using our elementary approach we present a new identity for the zeros of Bessel functions of the first kind, which in particular reduces to some other new identities. We also show that our method can be applied for the zeros of other special functions, like Struve functions of the first kind, and modified Bessel functions of the second kind. 相似文献
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Juri Rappoport 《PAMM》2007,7(1):2020017-2020018
In this paper the numerical Tau methods for the approximation of the kernels of Kontorovitch–Lebedev integral transforms are described. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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F.Alberto Grünbaum 《Journal of Mathematical Analysis and Applications》1973,41(1):115-121
We study a new type of inequality for Bessel functions. This is an analog of an inequality for Legendre polynomials, which plays an important role in studying the nonlinear Boltzmann equation. As an application of the Bessel case we treat the spherical functions associated with Minkowski space. 相似文献
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Árpád Baricz Dragana Jankov Maširević Saminathan Ponnusamy Sanjeev Singh 《Aequationes Mathematicae》2016,90(4):859-870
In this note our aim is to present some monotonicity properties of the product of modified Bessel functions of the first and second kind. Certain bounds for the product of modified Bessel functions of the first and second kind are also obtained. These bounds improve and extend known bounds for the product of modified Bessel functions of the first and second kind of order zero. A new Turán type inequality is also given for the product of modified Bessel functions, and some open problems are stated, which may be of interest for further research. 相似文献
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Simple inequalities for some integrals involving the modified Bessel functions Iν(x) and Kν(x) are established. We also obtain a monotonicity result for Kν(x) and a new lower bound, that involves gamma functions, for K0(x). 相似文献
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Á. Elbert 《Numerische Mathematik》1991,59(1):647-657
Summary LetC
vk be thekth positive zero of the cylinder functionC
v(x)=cosJ
v(x)–sinY
v(x), whereJ
v(x),Y
v(x) are the Bessel functions of first kind and second kind, resp., andv>0, 0<. Definej
vk byj
vk=C
vk with
. Using the notation 1/K=, we derive the first two terms of the asymptotic expansion ofj
vk in terms of the powers of at the expense of solving a transcendental equation. Numerical examples are given to show the accuracy of this approximation.Dedicated to the memory of Professor Lothar CollatzThis work has been supported by the Hungarian Scientific Grant No. 6032/6319 相似文献
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