Thiele's interpolation formula  In mathematics, Thiele's interpolation formula is a formula that defines a rational function formula_1 from a finite set of inputs formula_2 and their function values formula_3. 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: