منابع مشابه
On the Localization and Computation of Zeros of Bessel Functions
The topological degree of a continuous mapping is implemented for the calculation of the total number of the simple real zeros within any interval of the Bessel functions of first and second kind and their derivatives. A new algorithm, based on this implementation, is given for the localization and isolation of these zeros. Furthermore, a second algorithm is presented for their computation empl...
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Let jp „ denote the nth positive zero of J , p > 0. Then / ■■> 7\'/2 Jp.n > Oln + P) ■ We begin by considering the eigenvalue problem (1) -(•*/)' + x~y = X2x2p-Xy, X,p>0, (2) y(a) =y(\) = 0, 0 < a < 1. For simplicity of notation we will set q = p~x. It is easily verified that the general solution of (1) is y(x) = CxJq(Xqxx/q) + C2Yq(Xqxx'q) and that the eigenvalues are given by Jq(Xq)Yq(Xqax/q)...
متن کاملBounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros
Bounds for the distance |cν,s− cν±1,s′ | between adjacent zeros of cylinder functions are given; s and s′ are such that @cν,s′′ ∈ ]cν,s, cν±1,s′ [; cν,k stands for the kth positive zero of the cylinder (Bessel) function Cν(x) = cosαJν(x)− sinαYν(x), α ∈ [0, π[, ν ∈ R. These bounds, together with the application of modified (global) Newton methods based on the monotonic functions fν(x) = x2ν−1Cν...
متن کاملQuadrature formulae using zeros of Bessel functions as nodes
A gaussian type quadrature formula, where the nodes are the zeros of Bessel functions of the first kind of order α (<(α) > −1), was recently proved for entire functions of exponential type. Here we relax the restriction on α as well as on the function. Some applications are also given.
متن کاملZeros of the Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering
Some novel interlacing properties of the zeros for the Bessel and spherical Bessel functions are first presented and then applied to prove an interesting uniqueness result in inverse acoustic obstacle scattering. It is shown that in the resonance region, the shape of a sound-soft/sound-hard ball in R3 or a soundsoft/sound-hard disc in R2 is uniquely determined by a single far-field datum measur...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2003
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(02)00641-6