Abstract:Let [f0, . . . , fm] be a tuple of series in nonnegative powers of 1/z, fj(∞) = 0. It is supposed that the tuple is in "general position". We give a construction of type I and type II Hermite-Padé polynomials to the given tuple of degrees n and mn respectively and the corresponding (m + 1)-multi-indexes with the following property. Let M1(z) and M2(z) be two (m + 1) × (m + 1) polynomial matrices, M1(z), M2(z) ∈ GL(m + 1, C[z]), generated by type I and type II Hermite-Padé polynomials respectively. Then we hav… Show more
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