Abstract
When we define arithmetic and mathematical functions of series in the form h(x)=(x-c)^r(h_0+h_1(x-c)+h_2(x-c)^2+h_3(x-c)^3+…) by overloading in C++ programming language, the series can be treated as intrinsic numbers. Using this program, a function define for numerical computation can be expanded easily in this form. A numerical integration method is proposed for evaluating the definite integral of function having algebraic singularity: I(a, b)=∫^b_af(x)dx, f(x)=(x-a)^β(x-b)^ωg(x), β>-1 ω>-1 within a finite range[a, b]for a given function f(x)for application of this series. As a function f(x)can be expanded at x=a and x=b using this method, extended Euler-Maclaurin formula can be applied to the computation of this integral. This gives an effective numerical integration method. Numerical examples are also included to illustrate the performance of the present method.
