Expanding the function ln(1+ex) into power series in terms of the Dirichlet eta function and the Stirling numbers of the second kind

Keywords:
Dirichlet eta function, composite function, power series expansion, Stirling number of the second kind, Riemann zeta function, partial Bell polynomial
Published online:
2024-06-30
Abstract
In the paper, using several approaches, the authors expand the composite function ln(1+ex) into power series around x=0, whose coefficients are expressed in terms of the Dirichlet eta function η(1−n) and the Stirling numbers of the second kind S(n,k).
How to Cite
(1)
Li, W.-H.; Lim, D.; Qi, F. Expanding the Function ln(1+ex) into Power Series in Terms of the Dirichlet Eta Function and the Stirling Numbers of the Second Kind. Carpathian Math. Publ. 2024, 16, 320-327.