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\(q\)-blossoming and Hermite-Padé approximants to the \(q\)-exponential function. (English) Zbl 1379.41014
The paper deals with the problem of the Hermite-Padé approximation. The author provides new representations of the Hermite-Padé approximants in terms of the blossom of the partial sums of the exponential function. Then he generalizes these representations by expressing the Hermite-Padé approximants for the \(q\)-exponential function in terms of the \(q\)-blossom of its partial sums. These representations lead to a simple and elegant method for deriving explicit expressions for the approximants.

MSC:
41A21 Padé approximation
68U07 Computer science aspects of computer-aided design
Software:
Expokit
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