Three open problems and a conjecture

Huizeng Qin; Ovidiu Furdui

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page 187-196, electronic only
  • ISSN: 2391-5455

Abstract

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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].

How to cite

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Huizeng Qin, and Ovidiu Furdui. "Three open problems and a conjecture." Open Mathematics 13.1 (2015): 187-196, electronic only. <http://eudml.org/doc/275947>.

@article{HuizengQin2015,
abstract = {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].},
author = {Huizeng Qin, Ovidiu Furdui},
journal = {Open Mathematics},
keywords = {Multiple series; Polylogarithm function; Stirling numbers of the first kind; Riemann zeta function},
language = {eng},
number = {1},
pages = {187-196, electronic only},
title = {Three open problems and a conjecture},
url = {http://eudml.org/doc/275947},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Huizeng Qin
AU - Ovidiu Furdui
TI - Three open problems and a conjecture
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 187
EP - 196, electronic only
AB - 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].
LA - eng
KW - Multiple series; Polylogarithm function; Stirling numbers of the first kind; Riemann zeta function
UR - http://eudml.org/doc/275947
ER -

References

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  1. [1] Furdui O., Limits, Series and Fractional Part Integrals. Problems in Mathematical Analysis, Springer, New York, 2013 Zbl1279.26017
  2. [2] Boros G., Moll V.H., Irresistible Integrals, Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge University Press, Cambridge, 2004 Zbl1090.11075
  3. [3] Blümlein J., Broadhurst D.J., Vermaseren J.A.M., The multiple zeta value data mine, Comput. Phys. Commun., 2010, 181, 582–625 [WoS] Zbl1221.11183
  4. [4] Lewin L., Polylogarithms and Associated Functions, North-Holland, Amsterdam, 1981 Zbl0465.33001
  5. [5] Srivastava H.M., Choi J., Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, 2001 Zbl1014.33001
  6. [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 Zbl0828.11044
  7. [7] Bromwich T.J.I’A., An Introduction to the Theory of Infinite Series, 3rd ed., AMS Chelsea Publishing, Providence, Rhode Island, 1991 
  8. [8] Medina L.A., Moll V.H., A class of logarithmic integrals, Ramanujan J., 2009, 20, 91–126 [WoS] Zbl1180.33029
  9. [9] U. Abel, A solution to Open Problem 3.137 by O. Furdui on multiple factorial series [arXiv:1508.04315] 

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