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Riordan arrays and generalized Lagrange series

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Abstract

The theory of Riordan arrays studies the properties of formal power series and their sequences. The notion of generalized Lagrange series proposed in the present paper is intended to fill the gap in the methodology of this theory. Generalized Lagrange series appear in it implicitly, as various equalities. No special notation is provided for these series, although particular cases of these series are generalized binomial and generalized exponential series. We give the definition of generalized Lagrange series and study their relationship with ordinary Riordan arrays and, separately, with Riordan exponential arrays.

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  1. Mathematical Notes,” Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    E. V. Burlachenko

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  1. E. V. Burlachenko
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Correspondence to E. V. Burlachenko.

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Original Russian Text © E. V. Burlachenko, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 4, pp. 510–518.

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Burlachenko, E.V. Riordan arrays and generalized Lagrange series. Math Notes 100, 531–539 (2016). https://doi.org/10.1134/S0001434616090248

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