Let be a Reciprocal Difference. Then Thiele's interpolation formula is the Continued Fraction
References
Abramowitz, M. and Stegun, C. A. (Eds.).
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, p. 881, 1972.
Milne-Thomson, L. M. The Calculus of Finite Differences. London: Macmillan, 1951.