A divided difference expansion with remainder for a general divided difference is derived that contains Floater's recent derivative expansion as a special case.
Integral form of divided differences
โ Scribed by K. J. Overholt
- Publisher
- Springer Netherlands
- Year
- 1973
- Tongue
- English
- Weight
- 111 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0006-3835
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๐ SIMILAR VOLUMES
Divided differences are operators acting on functions of several variables. We ลฝ k describe this action on the basis of modified powers that is, x is replaced by ลฝ . ลฝ . ลฝ . i x y a xy a ะธะธะธ x y a . Special cases are of interest when a s q or 0 1 ny1 i a s i. แฎ 1999 Academic Press i 1. PRELIMINARIES
We define means in n variables by taking the intersection point in R n of n osculating hyperplanes to a given curve in R n . These planes are the natural extensions of the osculating plane in R 3 . More precisely, let C be a curve in R n , and let 0a -ะธะธะธa -ฯฑ. Let O be the osculating hyperplane to C