Transcendence of certain infinite sums involving rational functions

Marian Genčev

Acta Mathematica Universitatis Ostraviensis (2007)

  • Volume: 15, Issue: 1, page 7-14
  • ISSN: 1804-1388

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Genčev, Marian. "Transcendence of certain infinite sums involving rational functions." Acta Mathematica Universitatis Ostraviensis 15.1 (2007): 7-14. <http://eudml.org/doc/35167>.

@article{Genčev2007,
author = {Genčev, Marian},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {summation methods; infinite series; transcendence; summation methods; infinite series; transcendence},
language = {eng},
number = {1},
pages = {7-14},
publisher = {University of Ostrava},
title = {Transcendence of certain infinite sums involving rational functions},
url = {http://eudml.org/doc/35167},
volume = {15},
year = {2007},
}

TY - JOUR
AU - Genčev, Marian
TI - Transcendence of certain infinite sums involving rational functions
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2007
PB - University of Ostrava
VL - 15
IS - 1
SP - 7
EP - 14
LA - eng
KW - summation methods; infinite series; transcendence; summation methods; infinite series; transcendence
UR - http://eudml.org/doc/35167
ER -

References

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  2. Hancl J., Tijdeman R., On the irrationality of Cantor series, J. reine angew. Math., vol. 571, (2004), 145-158. Zbl1049.11076MR2070147
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  5. Hancl J., Tijdeman R., On the irrationality of polynomial Cantor series, Acta Arith., (to appear). MR2413364
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  10. Sebah P., Gourdon X., Introduction to the Gamma Function, available under http://www.numbers.computation.free.fr/Constants/constants.html. 
  11. Sondow J., Zudilin W., Euler's constant, q-logarithms, and formulas of Ramanujan and Gosper, available under http://arXiv:math.NT/0304021. Zbl1132.11056
  12. Sury B., Tianming Wang, Feng-Zhen Zao, Identities involving Reciprocals of Binomial Coefficients, Journal of Integer Sequences, Vol. 7 (2004), 1-12. MR2084860
  13. Tijdeman R., Some applications of diophantine approximation, Proc. Millennium Conference on Number Theory, Urbana, May 2000, to appear. Zbl1045.11022MR1956281
  14. Tijdeman R., Pingzhi Y., 10.1016/S0019-3577(02)80018-0, Indag. Mathem., N.S., 13 (3), (2002), 407-418. Zbl1018.11037MR2057056DOI10.1016/S0019-3577(02)80018-0
  15. Waldschmidt M., Transcendence de periodes: état des connaissances, African Diaspora Journal of Mathematics, Advances in Mathematics, Vol. 1 (2006), No. 2, available under http://arXiv.org/abs/math.NT/0502582. 

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