Comparative Analysis of Ultra-low Frequency Atmospheric Field Legendre Function Derivative Expressions
GAI Mingming
WEN Dong
XI Hailong
CHU Juan
Abstract：Ultra-low frequency communication atmosphere field strength calculation includes the first kind of Legendre function to the first derivative of the distance or contains the second derivative, the two derivative can be expressed as an infinite series, but infinite series calculation is under the control of the digits limit of the computer, so series computing can`t be used in high-end of ultra-low frequency.In addition, there are several approximation formula.But the approximate formula of applicable range and precision are unclear.So infinite series formulas and the approximate formula of three common are programmed and calculated by soft ware based on Matlab, comparing each other, the applicable condition and precision difference formula is determined.
Keywords：ultra-low frequencyatmospheric field strengthLegendre function to the first derivative of the distanceLegendre function to the second derivative of the distance
Publication Date：2017-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：5( 430-433,443 )