## A Collection of Examples of the Applications of the Calculus of Finite Differences: Suivi de Examples of the Solutions of Functional Equations |

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algebraic algebraic curves Appendix applying arbitrary constant arbitrary function binomial theorem Calculus of Differences circulating equation circulating functions class of curves conic section continued fraction deduced denoted determine developed in powers differential equation eliminating equal equation becomes equation of differences example Exponential Functions expression following equation formula functional equation given equation hence homogeneous function infinity instance integrate the equation inverse inverse function last problem logarithmic manner method multiple numbers comprised obtain ordinate parabola particular solution periodic function quantity radius of curvature reduce Required the difference resolve result roots roots of unity satisfy second member Sect shew shewn similar straight line substitution succeeding factors sum the series suppose symbols of operation symmetrical function tangents Taylor's theorem theorem theory of elimination tion vanish whence zero