Programs for the approximation of real and imaginary single- and multi-valued functions by means of Hermite–Padé-approximants Original Research Article

We present programs for the calculation and evaluation of special type Hermite–Padé-approximations. They allow the user to either numerically approximate multi-valued functions represented by a formal series expansion or to compute explicit approximants for them. The approximation scheme is based on Hermite–Padé polynomials and includes both Padé and algebraic approximants as limiting cases. The algorithm for the computation of the Hermite–Padé polynomials is based on a set of recursive equations which were derived from a generalization of continued fractions. The approximations retain their validity even on the cuts of the complex Riemann surface which allows for example the calculation of resonances in quantum mechanical problems. The programs also allow for the construction of multi-series approximations which can be more powerful than most summation methods.