The divided difference
on points , , ..., of a function is
defined by
and

(1) |

(2) | |||

(3) | |||

(4) |

Defining

(5) |

(6) |

(7) |

Consider the following question: does the property

(8) |

**References**

Abramowitz, M. and Stegun, C. A. (Eds.).
*Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.*
New York: Dover, pp. 877-878, 1972.

Aczél, J. ``A Mean Value Property of the Derivative of Quadratic Polynomials--Without Mean Values and
Derivatives.'' *Math. Mag.* **58**, 42-45, 1985.

Andersen, K. M. ``A Characterization of Polynomials.'' *Math. Mag.* **69**, 137-142, 1996.

Bailey, D. F. ``A Mean-Value Property of Cubic Polynomials--Without Mean Values.'' *Math. Mag.* **65**, 123-124, 1992.

Beyer, W. H. (Ed.) *CRC Standard Mathematical Tables, 28th ed.* Boca Raton, FL: CRC Press, pp. 439-440, 1987.

Schwaiger, J. ``On a Characterization of Polynomials by Divided Differences.'' *Aequationes Math.* **48**, 317-323, 1994.

© 1996-9

1999-05-24