Thiele's interpolation formula

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In mathematics, Thiele's interpolation formula is a formula that defines a rational function from a finite set of inputs and their function values . The problem of generating a function whose graph passes through a given set of function values is called interpolation. This interpolation formula is named after the Danish mathematician Thorvald N. Thiele. It is expressed as a continued fraction, where ρ represents the reciprocal difference:

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