Toothed whale porpoise as a fish. Toothed whales, as well as baleen whales, are descendants of land-dwelling mammals of the artiodactyl order (even-toed ungulates). They are closely related to the hippopotamus, sharing a common ancestor that lived around 54 million years ago (mya). The primitive cetaceans, or archaeocetes, first took to the sea approximately 49 mya and became fully aquatic by 5–10 million years later. The adaptation of echolocation and enhanced fat synthesis in blubber occurred when toothed whales split apart from baleen whales, and distinguishes modern toothed whales from fully aquatic archaeocetes. This happened around 34 mya. Unlike toothed whales, baleen
Divided differences "ƒ" on the nodes "x", ..., "x" are used: etc. Divided differences for formula_12 and the first few values of formula_13: To make the recursive process more clear, the divided differences can be put in a tabular form: The divided difference scheme can be put into an upper triangular matrix. Let formula_24. Then it holds formula_44 With the help of a polynomial function formula_45 with formula_46 this can be written as Alternatively, we can allow counting backwards from the start of the sequence by defining formula_48 whenever formula_49 or formula_50. This definition allows formula_51 to be interpreted as formula_52, formula_53