  A "blendstring" is a piecewise polynomial interpolant with high-degree
two-point Hermite interpolational polynomials on each piece, analogous to a
cubic spline. Blendstrings are smoother and can be more accurate than cubic
splines, and can be used to represent smooth functions on a line segment or
polygonal path in the complex plane. I sketch some properties of blendstrings,
including efficient methods for evaluation, differentiation, and integration,
as well as a prototype Maple implementation. Blendstrings can be differentiated
and integrated exactly and can be combined algebraically. I also show
applications of blendstrings to solving differential equations and computing
Mathieu functions and generalized Mathieu eigenfunctions.
