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Shanks’ convergence acceleration transform, Padé approximants and partitions. (English) Zbl 0617.41030
Shanks developed a method for accelerating the convergence of sequences. When applied to classical sequences in number theory, Shanks’ transform yields some famous identities of Euler and Gauss. It is shown here that the Padé approximants for the little q-Jacobi polynomials can be used to explain and extend Shanks’ observations. The combinatorial significance of these results is also discussed.

MSC:
41A20 Approximation by rational functions
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