| Title:
|
Transcendence of certain infinite sums involving rational functions (English) |
| Author:
|
Genčev, Marian |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
15 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
7-14 |
| . |
| Category:
|
math |
| . |
| Keyword:
|
summation methods |
| Keyword:
|
infinite series |
| Keyword:
|
transcendence |
| MSC:
|
11J81 |
| idZBL:
|
Zbl 1234.11094 |
| idMR:
|
MR2418777 |
| . |
| Date available:
|
2009-12-29T09:21:53Z |
| Last updated:
|
2015-03-15 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137490 |
| . |
| Reference:
|
[1] Adhikari S. D., Saradha N., Shorey T. N., Tijdeman R.: Transcendental infinite sums.Indag. Math., New Ser. 12, no. 1, (2001), 1-14. Zbl 0991.11043, MR 1908135, 10.1016/S0019-3577(01)80001-X |
| Reference:
|
[2] Hancl J., Tijdeman R.: On the irrationality of Cantor series.J. reine angew. Math., vol. 571, (2004), 145-158. Zbl 1049.11076, MR 2070147 |
| Reference:
|
[3] Hancl J., Tijdeman R.: On the rationality of Cantor and Ahmes series.Publicat. Math. 65, no. 3-4, (2004), 371-380. MR 2107954 |
| Reference:
|
[4] Hancl J., Tijdeman R.: On the irrationality of factorial series.Acta Arith. vol. 118, no. 4, (2005), 383-401. Zbl 1088.11054, MR 2165552, 10.4064/aa118-4-5 |
| Reference:
|
[5] Hancl J., Tijdeman R.: On the irrationality of polynomial Cantor series.Acta Arith., (to appear). MR 2413364 |
| Reference:
|
[6] Lehmer D. H.: Euler constants for arithmetical progressions.Acta Arithmetica 27, (1975), 125-142. Zbl 0302.12003, MR 0369233 |
| Reference:
|
[7] Parshin A. N., Shafarevich I. R. (Eds.): Encyclopaedia of Mathematical Sciences.volume 44, Number Theory IV, Springer-Verlag Berlin Heidelberg, 1998. MR 1603604 |
| Reference:
|
[8] Rektorys K., a spol.: Přehled užité matematiky.SNTL, Prague, 1963. Zbl 0175.15801, MR 0158576 |
| Reference:
|
[9] Saradha N., Tijdeman R.: On the transcendence of infinite sums of values of rational functions.J. London Math. Soc. (3) 67 (2003), 580-592. Zbl 1045.11051, MR 1967693, 10.1112/S0024610702003988 |
| Reference:
|
[10] Sebah P., Gourdon X.: Introduction to the Gamma Function.available under http://www.numbers.computation.free.fr/Constants/constants.html. |
| Reference:
|
[11] Sondow J., Zudilin W.: Euler's constant, q-logarithms, and formulas of Ramanujan and Gosper.available under http://arXiv:math.NT/0304021. Zbl 1132.11056 |
| Reference:
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[12] Sury B., Tianming Wang, Feng-Zhen Zao: Identities involving Reciprocals of Binomial Coefficients.Journal of Integer Sequences, Vol. 7 (2004), 1-12. MR 2084860 |
| Reference:
|
[13] Tijdeman R.: Some applications of diophantine approximation.Proc. Millennium Conference on Number Theory, Urbana, May 2000, to appear. Zbl 1045.11022, MR 1956281 |
| Reference:
|
[14] Tijdeman R., Pingzhi Y.: On the rationality of Cantor and Ahmes series.Indag. Mathem., N.S., 13 (3), (2002), 407-418. Zbl 1018.11037, MR 2057056, 10.1016/S0019-3577(02)80018-0 |
| Reference:
|
[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. |
| . |
