Cubic and quartic series with the tail of \(\ln 2\)

Ovidiu Furdui; Alina Sîntămărian

doi:10.56754/0719-0646.2501.089

Authors

Ovidiu Furdui Department of Mathematics Technical University of Cluj-Napoca Str. Memorandumului Nr. 28, 400114 Cluj-Napoca, Romania. https://orcid.org/0000-0002-3259-7740
Alina Sîntămărian Department of Mathematics Technical University of Cluj-Napoca Str. Memorandumului Nr. 28, 400114 Cluj-Napoca, Romania. https://orcid.org/0000-0003-3105-1778

MSC:

40A05, 40C10

DOI:

https://doi.org/10.56754/0719-0646.2501.089

Keywords:

Abel’s summation formula, cubic series, quartic series, tail of ln 2

Abstract

In this paper we calculate some remarkable cubic and quartic series involving the tail of \(\ln 2\). We also evaluate several linear and quadratic series with the tail of \(\ln 2\).

References

B. C. Berndt, Ramanujan’s notebooks. Part I, New York: Springer-Verlag, 1985.

K. N. Boyadzhiev, “Power series with skew-harmonic numbers, dilogarithms, and double integrals”, Tatra Mt. Math. Publ., vol. 56, no. 1, pp. 93–108, 2013.

O. Furdui, Limits, Series and Fractional Part Integrals, Problems in Mathematical Analysis, New York: Springer, 2013.

O. Furdui and A. Sîntamărian, “Alternating quadratic and cubic series with the tail of ln 2”, Creat. Math. Inform., to be published.

A. Sîntamărian and O. Furdui, Sharpening mathematical analysis skills, Problem Books in Mathematics, Cham: Springer, 2021.