Modified approximation algorithm of second-class Bessel function high-order power infinite series

Abstract

The invention discloses a modified approximation algorithm of second-class Bessel function high-order power infinite series and relates to the mathematical and signal processing field. The algorithm comprises following steps: a, firstly, giving a finite order Q'; calculating auxiliary coefficients a0, a1, ..., aQ; according to the power of the second-class Bessel function, setting a finite order Q, calculating main coefficients c0, c1, ..., cQ; and then, giving different powers and finite orders and generating a reference table related to the main coefficients c0, c1, ..., cQ to serve as pre-known data. According to the invention, a corrected finite series representation framework of the higher power of the second-class Bessel function is given; the pre-generated main coefficients c0, c1,..., cQ are substituted into the framework to easily obtain a corrected finite series representation form of the higher power of the second-class Bessel function, and finally, the accuracy of series approximation representation is proved through an application example analysis based on Bessel function higher power series approximation in a wireless communication system.

Description

technical field [0001] The invention belongs to the field of mathematics and signal processing, and in particular relates to an approximation algorithm for an infinite series of high-power infinite series of a modified Bessel function of the second type, and is especially suitable for further processing when the high-power of the modified Bessel function appears. Occasions where mathematical calculations (such as integrals) are not readily available. Background technique [0002] In view of some possible theoretical and practical applications, mathematical calculations that need to be applied to finite series of high powers of modified Bessel functions of the second type, such as integrals, are difficult to obtain simplified closed-form analytical mathematical expressions. Through the investigation of the current literature, there are few literatures that study the finite series representation of the first power of the second-order Bessel function, and there is no reference ...

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Problems solved by technology

The challenge of Bessel function high power finite series representation is that the second type of first-order Bessel function near the zero point on the abscissa has a larger value, and a small error in the first power will cause a larger value in the high power. The approximation error of , it is necessary to study the effective finite order approximation model of the high power of the Bessel function

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