A study on the limiting ratio of consecutive terms in a class of bivariate generating functions
A class of bivariate quadratic functions and its induced generating functions are studied in the paper. The author shows that under some conditions, the sequence of quotients obtained from the ratios of the consecutive terms in the generating function converges. In particular, letting the quotient be 1 yields a tangent line to the original bivariate quadratic curve at a point in the x-axis. The point is the only one at which the line intersects the curve, and is either the only one or the closer one (to the origin) at which the curve intersects the x-axis. Numerical examples are provided to illustrate the work.
limiting ratio generating function quadratic bivariate function