DocumentCode :
1438824
Title :
Asymptotic Expansion of the Associated Legendre Function Over the Interval 
Author :
Gardner, J.S.
Volume :
59
Issue :
4
fYear :
2011
fDate :
4/1/2011 12:00:00 AM
Firstpage :
1424
Lastpage :
1427
Abstract :
The associated Legendre function is generally defined by an integral or differential equation. However, a closed-form representation of the associated Legendre function of order 0 or 1 could be beneficial to model the propagation and scattering of waves in spherical coordinates. To this end, an associated Legendre approximation with accuracy over the entire defining interval is presented that is particularly conducive to integral evaluation using stationary phase or steepest descents.
Keywords :
approximation theory; differential equations; electromagnetic wave propagation; electromagnetic wave scattering; gradient methods; integral equations; associated Legendre approximation; asymptotic expansion; differential equation; integral equation; spherical coordinates; stationary phase; steepest descents; waves propagation; waves scattering; Accuracy; Approximation methods; Differential equations; Electromagnetics; Harmonic analysis; Integral equations; Scattering; Asymptotic expansion; Legendre; coalesce; saddle point; stationary phase; steepest descents;
fLanguage :
English
Journal_Title :
Antennas and Propagation, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-926X
Type :
jour
DOI :
10.1109/TAP.2011.2109354
Filename :
5704556
Link To Document :
