An Extended Table of Zeros of Cross Products of Bessel Functions

Item

Title
An Extended Table of Zeros of Cross Products of Bessel Functions
Date
1966
Index Abstract
Not Available
Photo Quality
Not Needed
Report Number
ARL 66-0023
Creator
Fettis, Henry E.
Caslin, James C.
Corporate Author
Applied Mathematics Research Laboratory
Laboratory
Aerospace Research Laboratories
Extent
126
Identifier
AD0637474
AD0637474
Access Rights
Distribution of this document is unlimited
Distribution Classification
1
Contract
Laboratory Research - No Contract
DoD Project
7071
DTIC Record Exists
Yes
Distribution Change Authority Correspondence
None
Distribution Conflict
No
Report Availability
Full text available
Date Issued
1966-02
Abstract
The report contains tables of the first five roots of the following transcendental equations:
(a) J0(α) Y0(kα) = Y0(α) J0(kα) (b) J1(α) Y1(kα) = Y1(α) J1(kα) (c) J0(α) Y1(kα) = Y0(α) J1(kα)
where J0(α), Y0(α), J1(α), Y1(α) are Bessel functions of order 0 and 1 respectively. In these equations, α is the unknown and k is a parameter which may assume any positive value, other than 0 or 1. However, because of symmetry, it is sufficient in the first two cases to tabulate the roots only for 0 < k < 1. Following a suggestion of Bogert [1]*, additional tables are included listing an auxiliary quantity γ which is better suited to interpolation particularly when k is close to unity. The auxiliary function is defined in the three cases as follows:
cases (a) and (b): γn=((1-k)/nπ)αn;
case (c): γn=(|k-1|)/(n-1/2)π)αn,
where αn (n= 1,2,3...) is any root of the equation applicable to the case considered. The function γn has the important property that
Limγn=1k->1
Date Modified
Scanned by request 1/18/2018 submitted by Federal University of Technology, Minna (University - International)
Provenance
Bearcat
Type
report
Format
1 online resource
Media
ARL66-0023.pdf

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