Interlacing of positive real zeros of Bessel functions
نویسندگان
چکیده
منابع مشابه
interlacing Properties of the Zeros of the Error Functions
Let (u&L1 , +, and C,!J be given functions in C(i), where 1 is some fixed Gnitc interval, and let do be a finite nonatomic strictly positive measure on .L For p E [I, co], we denote by E,(#) and E,(G) the error functions in the best P-approximation to (band #, respectively, from [ul ,...+,I (--spanjul ,...,&]). For p < CO, the D-approximation is taken with respect to the measure da, For p = co,...
متن کاملInterlacing Properties of Real Zeros of General Laguerre Polynomials
L (↵) n (x) for arbitrary real ↵. Such results are well-known in the case ↵ > 1. In the case 2 < ↵ < 1, we use a mixed 3-term recurrence relation to show, for example, that, apart from a single value of ↵, the (all real) zeros of (x + ↵ + 1)L n (x) interlace with those of xL n (x). By studying the changes in interlacing that occur when ↵ decreases through the negative integer values 1, 2, . . ....
متن کاملOn 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 کاملBounds for the small real and purely imaginary zeros of Bessel and related functions
We give two distinct approaches to finding bounds, as functions of the order ν, for the smallest real or purely imaginary zero of Bessel and some related functions. One approach is based on an old method due to Euler, Rayleigh, and others for evaluating the real zeros of the Bessel function Jν(x) when ν > −1. Here, among other things, we extend this method to get bounds for the two purely imagi...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2011
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2010.09.024