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...
متن کاملLower Bounds for the Zeros of Bessel Functions
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 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 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 کاملOn two-dimensional Bessel functions
The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal lines.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1978
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1978-0481160-x