摘要
In this paper, we show that if a problem of (0, 1, ..,m - 2, m) ─ interpolation on the zeros of (1 -x)p:tf' (x) (a>1,β≥- 1 ) has an infinity of solutions then the general form of the so-lutions is f0(x) +Cf(x) with an arbitrary constant C,where p:tf' (x) stands for the (n- 1 )th Jacobi polynomial, and f0 (x) and f(x) are fixed polynomials of degree ≤mn - 1,and, meanwhile. the explicit form of f(x) is given. Moreover, a necessary and sufficient condition of quadrature regularity of the interpolation in a manageable form is established
In this paper, we show that if a problem of (0, 1, ..,m - 2, m) ─ interpolation on the zeros of (1 -x)p:tf' (x) (a>1,β≥- 1 ) has an infinity of solutions then the general form of the so-lutions is f0(x) +Cf(x) with an arbitrary constant C,where p:tf' (x) stands for the (n- 1 )th Jacobi polynomial, and f0 (x) and f(x) are fixed polynomials of degree ≤mn - 1,and, meanwhile. the explicit form of f(x) is given. Moreover, a necessary and sufficient condition of quadrature regularity of the interpolation in a manageable form is established
