共查询到20条相似文献,搜索用时 15 毫秒
1.
rpd Baricz 《Expositiones Mathematicae》2008,26(3):279-293
In this paper, we extend some known elementary trigonometric inequalities, and their hyperbolic analogues to Bessel and modified Bessel functions of the first kind. In order to prove our main results, we present some monotonicity and convexity properties of some functions involving Bessel and modified Bessel functions of the first kind. We also deduce some Turán and Lazarević-type inequalities for the confluent hypergeometric functions. 相似文献
2.
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
3.
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
4.
Biserka Draš?i? Tibor K. Pogány 《Journal of Mathematical Analysis and Applications》2005,308(2):775-780
A first kind Fredholm integral equation with nondegenerate kernel is given, which particular solution is the Bessel function of the first kind. This equation is solved by means of Mellin transform pair. 相似文献
5.
Richard Askey 《Proceedings Mathematical Sciences》1990,100(1):1-8
Let μ k,n denote the relative maxima of ?Q n(x)?, the Legendre function of the second kind, ordered so that μ k+1,n occurs to the left of μ k,n . They by analogy with a theorem of Szegö for Legendre polynomials, μ k,n +1<μ k,n ,k=1,...,n,n=1,2,... 相似文献
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In this paper, we define a class of strongly connected digraph, called the k-walk- regular digraph, study some properties of it, provide its some algebraic characterization and point out that the 0-walk-regular digraph is the same as the walk-regular digraph discussed by Liu and Lin in 2010 and the D-walk-regular digraph is identical with the weakly distance-regular digraph defined by Comellas et al in 2004. 相似文献
8.
Ling Zhu 《Applied mathematics and computation》2011,217(21):8504-8506
In this note, new sharpened Redheffer type inequalities involving modified Bessel functions are established. 相似文献
9.
A collocation method based on the Bessel functions of the first kind for singular perturbated differential equations and residual correction 下载免费PDF全文
Şuayip Yüzbaşı 《Mathematical Methods in the Applied Sciences》2015,38(14):3033-3042
In this paper, a collocation method is given to solve singularly perturbated two‐point boundary value problems. By using the collocation points, matrix operations and the matrix relations of the Bessel functions of the first kind and their derivatives, the boundary value problem is converted to a system of the matrix equations. By solving this system, the approximate solution is obtained. Also, an error problem is constructed by the residual function, and it is solved by the presented method. Thus, the error function is estimated, and the approximate solutions are improved. Finally, numerical examples are given to show the applicability of the method, and also, our results are compared by existing results. Copyright © 2014 JohnWiley & Sons, Ltd. 相似文献
10.
We unify the three distinct inequality sequences (Abramowitz and Stegun (1972) [1, 9.5.2]) of positive real zeros of Bessel functions into a single one. 相似文献
11.
Edward Neuman 《Journal of Mathematical Analysis and Applications》2011,373(1):203-646
Computable bounds for the generalized complete elliptic integrals of the first and second kind are obtained. Also, bounds for some combinations and products for integrals under discussion are established. It has been proven that both families of integrals are logarithmically convex as functions of the first parameter. This property has been employed to obtain several inequalities involving integrals in question. 相似文献
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Recently Pogány and Süli (Proc. Amer. Math. Soc. 137 (7) (2009) 2363-2368) derived a closed-form integral expression for Neumann series of Bessel functions. In this note we precisely characterize the class of functions α that generate the integral representation of a Neumann series of Bessel functions in the sense that the restriction αN|=(αn) of a function α to the set N of all positive integers is the sequence of coefficients of the initial Neumann series. 相似文献
15.
Christer O.Kiselman 《中国科学A辑(英文版)》2005,48(Z1)
We study discrete analogues of holomorphic functions of one and two variables, especially those that were called monodiffric functions of the first kind by Rufus Isaacs. Discrete analogues of the Cauchy-Riemann operators, domains of holomorphy in one discrete variable, and the Hartogs phenomenon in two discrete variables are investigated. 相似文献
16.
Vladimir Varlamov 《Journal of Mathematical Analysis and Applications》2010,370(2):687-1648
A new integral representation of the Hankel transform type is deduced for the function Fn(x,Z)=Zn−1Ai(x−Z)Ai(x+Z) with x∈R, Z>0 and n∈N. This formula involves the product of Airy functions, their derivatives and Bessel functions. The presence of the latter allows one to perform various transformations with respect to Z and obtain new integral formulae of the type of the Mellin transform, K-transform, Laplace and Fourier transform. Some integrals containing Airy functions, their derivatives and Chebyshev polynomials of the first and second kind are computed explicitly. A new representation is given for the function 2|Ai(z)| with z∈C. 相似文献
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This article proposes a simple efficient direct method for solving Volterra integral equation of the first kind. By using block-pulse functions and their operational matrix of integration, first kind integral equation can be reduced to a linear lower triangular system which can be directly solved by forward substitution. Some examples are presented to illustrate efficiency and accuracy of the proposed method. 相似文献
19.
B. V. Pal’tsev 《Mathematical Notes》1999,65(5):571-581
Bounds uniform in the real argument and the index for the functionsa
ν
(x)=xI′
ν
(x)/I′
ν
(x) andb
ν
(x)=xK′
ν
(x)/K
ν
(x), as well as for the modified Bessel functionsI
ν(x) andK
ν(x), are established in the quadrantx>0, ν≥0, except for some neighborhoods of the pointx=0, ν=0.
Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 681–692, May, 1999. 相似文献
20.
Javier Segura 《Journal of Mathematical Analysis and Applications》2011,374(2):516-528
New sharp inequalities for the ratios of Bessel functions of consecutive orders are obtained using as main tool the first order difference-differential equations satisfied by these functions; many already known inequalities are also obtainable, and most of them can be either improved or the range of validity extended. It is shown how to generate iteratively upper and lower bounds, which are converging sequences in the case of the I-functions. Few iterations provide simple and effective upper and lower bounds for approximating the ratios Iν(x)/Iν−1(x) and the condition numbers for any x,ν?0; for the ratios Kν(x)/Kν+1(x) the same is possible, but with some restrictions on ν. Using these bounds Turán-type inequalities are established, extending the range of validity of some known inequalities and obtaining new inequalities as well; for instance, it is shown that Kν+1(x)Kν−1(x)/(Kν2(x))<|ν|/(|ν|−1), x>0, ν∉[−1,1] and that the inequality is the best possible; this proves and improves an existing conjecture. 相似文献