scholarly journals The zeros of bessel functions.

1918 ◽  
Vol 94 (659) ◽  
pp. 190-206 ◽  
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
Practical Importance ◽  
Zeros Of Bessel Functions ◽  
Order Of Magnitude ◽  
Low Order

1. Although many results are known concerning the zeros of Bessel functions,* the greater number of these results are of practical importance only in the case of functions of comparatively low order. For example, McMahon has given a formula† for calculating the zeros of the Bessel function J n ( x ), namely that, if k 1 , k 2 , k 3 , ..., are the positive zeros arranged in ascending order of magnitude, then ks = β- 4 n 2 -1/8β - 4(4 n 2 -1)(28 n 2 -31)/3.(8β) 3 -..., where β = 1/4 π (2 n +4 s —1).

scholarly journals On some infinite series involving the zeros of Bessel functions of the first kind

1960 ◽  
Vol 4 (3) ◽  
pp. 144-156 ◽  
Author(s):  
Ian N. Sneddon
Keyword(s):  
Positive Integer ◽  
Bessel Function ◽  
Rational Function ◽  
Recurrence Relation ◽  
Infinite Series ◽  
Bessel Functions ◽  
Zeros Of Bessel Functions ◽  
Image Position

In this paper we shall be concerned with the derivation of simple expressions for the sums of some infinite series involving the zeros of Bessel functions of the first kind. For instance, if we denote by γv, n (n = l, 2, 3,…) the positive zeros of Jv(z), then, in certain physical applications, we are interested in finding the values of the sumsandwhere m is a positive integer. In § 4 of this paper we shall derive a simple recurrence relation for S2m,v which enables the value of any sum to be calculated as a rational function of the order vof the Bessel function. Similar results are given in § 5 for the sum T2m,v.

scholarly journals The radius of convexity of normalized Bessel functions of the first kind

2014 ◽  
Vol 12 (05) ◽  
pp. 485-509 ◽  
Author(s):  
Árpád Baricz ◽  
Róbert Szász
Keyword(s):  
Bessel Function ◽  
Unit Disk ◽  
Bessel Functions ◽  
Positive Zero ◽  
Open Unit ◽  
Open Unit Disk ◽  
Optimal Parameters ◽  
Zeros Of Bessel Functions ◽  
Radius Of Convexity

In this paper, we determine the radius of convexity for three kinds of normalized Bessel functions of the first kind. In the mentioned cases the normalized Bessel functions are starlike-univalent and convex-univalent, respectively, on the determined disks. The key tools in the proofs of the main results are some new Mittag-Leffler expansions for quotients of Bessel functions of the first kind, special properties of the zeros of Bessel functions of the first kind and their derivative, and the fact that the smallest positive zeros of some Dini functions are less than the first positive zero of the Bessel function of the first kind. Moreover, we find the optimal parameters for which these normalized Bessel functions are convex in the open unit disk. In addition, we disprove a conjecture of Baricz and Ponnusamy concerning the convexity of the Bessel function of the first kind.

On the Square of the Zeros of Bessel Functions

1984 ◽  
Vol 15 (1) ◽  
pp. 206-212 ◽  
Author(s):  
Árpád Elbert ◽  
Andrea Laforgia
Keyword(s):  
Bessel Functions ◽  
Zeros Of Bessel Functions

Higher monotonicity properties of normalized Bessel functions

2014 ◽  
Vol 12 (05) ◽  
pp. 1461007
Author(s):  
Yongping Liu
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
Positive Zero ◽  
Local Maxima ◽  
Monotonicity Properties

Denote by Jν the Bessel function of the first kind of order ν and μν,k is its kth positive zero. For ν > ½, a theorem of Lorch, Muldoon and Szegö states that the sequence [Formula: see text] is decreasing, another theorem of theirs states that the sequence [Formula: see text] has higher monotonicity properties. In the present paper, we proved that when ν > ½ the sequence [Formula: see text] has higher monotonicity properties and the properties imply those of the sequence of the local maxima of the function x-ν+1|Jν-1(x)|, x ∈ (0, ∞), i.e. the sequence [Formula: see text] has higher monotonicity properties.

On the zeros of Bessel functions. - IV

1978 ◽  
Vol 21 (15) ◽  
pp. 531-534 ◽  
Author(s):  
S. Ahmed ◽  
F. Calogero
Keyword(s):  
Bessel Functions ◽  
Zeros Of Bessel Functions

On the Convexity of the Zeros of Bessel Functions

1985 ◽  
Vol 16 (3) ◽  
pp. 614-619 ◽  
Author(s):  
Árpád Elbert ◽  
Andrea Laforgia
Keyword(s):  
Bessel Functions ◽  
Zeros Of Bessel Functions

scholarly journals Higher monotonicity properties and inequalities for zeros of Bessel functions

1991 ◽  
Vol 112 (2) ◽  
pp. 513-513 ◽  
Author(s):  
Laura Nicol{ò-Amati Gori ◽  
Andrea Laforgia ◽  
Martin E. Muldoon
Keyword(s):  
Bessel Functions ◽  
Zeros Of Bessel Functions ◽  
Monotonicity Properties
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