(0, 1, … ,m - 2, m) Interpolation on the Zeros of xL（a）n－1(x)

Abstract:

      A necessary and sufficient condition for regularity of (0, 1, …, m - 2, m) in-terpolation on the zeros of xL^（a）_n－1（x）(a>-1 ) in a nianagealbe form is established, where xL^（a）_n－1（x） is the (n-1)- th Laguerre polynomial . Meanwhile, the explicit representationof the fundamental polynomials, when they exist, is given. Moreover, we show that if theproblem of (0, 1, …, m - 2, m) interpolation has an infinity of solutions then the generalform of the solutions is f₀（ｘ）＋Ｃｆ₁（ｘ） with an arbitrary constant C.