Three open problems and a conjecture

• Autorzy: Huizeng Qin , Ovidiu Furdui
• Języki publikacji: EN

Abstrakty

EN

In this paper we solve three open problems and a conjecture related to the calculations of some classes of multiple series posed by Furdui in [1].

Słowa kluczowe

EN

Multiple series; Polylogarithm function; Stirling numbers of the first kind; Riemann zeta function

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-06-03

zaakceptowano

2015-10-16

online

2015-10-30

Twórcy

autor

Huizeng Qin

• School of Science, Shandong University of Technology, Zibo, Shandong, 255049, China

autor

Ovidiu Furdui

• School of Science, Shandong University of Technology, Zibo, Shandong, 255049, China

Bibliografia

• [1] Furdui O., Limits, Series and Fractional Part Integrals. Problems in Mathematical Analysis, Springer, New York, 2013
• [2] Boros G., Moll V.H., Irresistible Integrals, Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge University Press, Cambridge, 2004
• [3] Blümlein J., Broadhurst D.J., Vermaseren J.A.M., The multiple zeta value data mine, Comput. Phys. Commun., 2010, 181, 582–625 [WoS]
• [4] Lewin L., Polylogarithms and Associated Functions, North-Holland, Amsterdam, 1981
• [5] Srivastava H.M., Choi J., Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, 2001
• [6] Li-Chien S., Remarks on some integrals and series involving the Stirling numbers and ξ(n), Trans. Am. Math. Soc., 1995, 347 (4), 1391–1399
• [7] Bromwich T.J.I’A., An Introduction to the Theory of Infinite Series, 3rd ed., AMS Chelsea Publishing, Providence, Rhode Island, 1991
• [8] Medina L.A., Moll V.H., A class of logarithmic integrals, Ramanujan J., 2009, 20, 91–126 [WoS]
• [9] U. Abel, A solution to Open Problem 3.137 by O. Furdui on multiple factorial series [arXiv:1508.04315]

Identyfikatory

DOI

10.1515/math-2015-0069