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Lagrange interpolating polynomial

Let $(a_{0},b_{0})$, $(a_{1},b_{1})$, $\ldots $, $(a_{n}$,$b_{n})$ be $n+1$ points in the plane, with all the $a_{i}$ distinct. The Lagrange interpolating polynomial is the polynomial of degree $n$ given by the formula MATH

Its graph passes through the $n+1$ points $(a_{0},b_{0})$, $(a_{1},b_{1})$, $\ldots $, $(a_{n}$,$b_{n})$. This formula was described by the English mathematician Edward Waring in 1779, rediscovered by Euler in 1783, and published by Lagrange in 1795.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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