Numerical Integration Method for Cauchy Principal-Value Integrals by Taylor Seires

Abstract

Abstract. The arithmetic operations and functions for Taylor series can be definedeasily, and programming is easy. With these programs, the function defined by arithmetic operations,fundamental functions, conditional statements, etc. can be easily expanded to Taylor series. With these Taylor series, Cauchy principal-Value integrals can be divided into the improper integrals and the regular integrals with singularity on appearance. If the integrals with singularity can be calculated analytically and numerical integration of the regular integrals can be carried out easily, the effective numerical integration methods for these improper integrals will be obtained.