Reciprocal Difference
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In mathematics, the reciprocal difference of a
finite sequence In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called th ...
of numbers (x_0, x_1, ..., x_n) on a function f(x) is defined inductively by the following formulas: :\rho_1(x_1, x_2) = \frac :\rho_2(x_1, x_2, x_3) = \frac + f(x_2) :\rho_n(x_1,x_2,\ldots,x_)=\frac+\rho_(x_2,\ldots,x_)


See also

*
Divided differences In mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions. Charles Babbage's difference engine, an early mechanical calculator, was designed to use this algorithm in its o ...


References

* *{{cite book, last=Abramowitz, first=Milton, author2=Irene A. Stegun, title= Handbook of Mathematical Functions, origyear=1964, year=1972, publisher=Dover, edition=ninth Dover printing, tenth GPO printing, isbn=0-486-61272-4, pag
878
} Finite differences