Logarithm of binomial series: Extension of a series of Knuth

Wenchang Chu

Vol. 24 No. 1 (2019)

Regular Articles

Logarithm of binomial series: Extension of a series of Knuth

Published 2018-10-08

Wenchang Chu

Wenchang Chu
Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Universit`a del Salento

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Abstract

The Lagrange expansion formula is employed to determine the Maclaurin series for the logarithms of Lambert’s series of binomial coefficients, extending the log–squared of the Catalan generating function due to Knuth (2015).

Keywords

Catalan numbers, Harmonic numbers, Elementary symmetric function, Bell polynomial, Lagrange expansion formula.

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Author Biography

Wenchang Chu

Professor

Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Universit`a del Salento