| (0, 1, … ,m - 2, m) Interpolation on the Zeros of xL（a）n－1(x) |
| Received:July 25, 1993 |
| Key Words:
Birkhoff interpolation Laguerre Polynomial regularity.
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| Fund Project:Project Supported by National Natural Science Foundation of China. |
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| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1995.03.001 |
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