Acta mathematica scientia,Series B ›› 1994, Vol. 14 ›› Issue (4): 400-408.
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Shi Yingguang
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Abstract: In this paper, we show that if a problem of (0, 1,..,m-2, m) -interpolation on the zeros of (1 -x)Pm-1(α,β)(x)(α>1,β ≥ -1) has an infinity of solutions then the general form of the solutions is f0(x) +Cf(x) with an arbitrary constant C,where Pm-1(α,β)(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.
Shi Yingguang. SINGULARITY AND QUADRATURE REGULARITY OF(0,1,…,m-2,m)-INTERPOLATION ON THE ZEROS OF(1-x) Pn-1(α,β)(x)[J].Acta mathematica scientia,Series B, 1994, 14(4): 400-408.
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