A theorem on irrationality of infinite series and applications
Acta Arithmetica (1993)
- Volume: 63, Issue: 4, page 313-323
- ISSN: 0065-1036
Access Full Article
topHow to cite
topC. Badea. "A theorem on irrationality of infinite series and applications." Acta Arithmetica 63.4 (1993): 313-323. <http://eudml.org/doc/206523>.
@article{C1993,
author = {C. Badea},
journal = {Acta Arithmetica},
keywords = {irrationality; rationality; inequalities; equalities; recurrence relation; convergent infinite series; sum of reciprocals; Oppenheim expansions},
language = {eng},
number = {4},
pages = {313-323},
title = {A theorem on irrationality of infinite series and applications},
url = {http://eudml.org/doc/206523},
volume = {63},
year = {1993},
}
TY - JOUR
AU - C. Badea
TI - A theorem on irrationality of infinite series and applications
JO - Acta Arithmetica
PY - 1993
VL - 63
IS - 4
SP - 313
EP - 323
LA - eng
KW - irrationality; rationality; inequalities; equalities; recurrence relation; convergent infinite series; sum of reciprocals; Oppenheim expansions
UR - http://eudml.org/doc/206523
ER -
References
top- [AnJ1] R. André-Jeannin, Irrationalité de la somme des inverses de certaines suites récurrentes, C. R. Acad. Sci. Paris Sér. I 308 (1989), 539-541. Zbl0682.10025
- [AnJ2] R. André-Jeannin, A note on the irrationality of certain Lucas infinite series, Fibonacci Quart., to appear.
- [Bad] C. Badea, The irrationality of certain infinite series, Glasgow Math. J. 29 (1987), 221-228. Zbl0629.10027
- [BuP] P. Bundschuh und A. Pethö, Zur Transzendenz gewisser Reihen, Monatsh. Math. 104 (1987), 199-223. Zbl0601.10025
- [Cuc] R. Cuculière, Problem E 2922, Amer. Math. Monthly 89 (1982), 63; solution, Amer. Math. Monthly 91 (1984), 435.
- [DaS] J. L. Davison and J. O. Shallit, Continued fractions for some alternating series, Monatsh. Math. 111 (1991), 119-126. Zbl0719.11038
- [Erd] P. Erdős, Some problems and results on the irrationality of the sum of infinite series, J. Math. Sci. 10 (1975), 1-7.
- [ErG] P. Erdős and R. L. Graham, Old and New Problems and Results in Combinatorial Number Theory, Monograph. Enseign. Math. 28, Genève 1980.
- [ErS] P. Erdős and E. G. Straus, On the irrationality of certain Ahmes series, J. Indian Math. Soc. 27 (1963), 129-133. Zbl0131.04902
- [Gal] J. Galambos, The Representation of Real Numbers by Infinite Series, Lecture Notes in Math. 502, Springer, 1976.
- [Han] D. Hanson, On the product of the primes, Canad. Math. Bull. 15 (1975), 33-37. Zbl0231.10008
- [Kui] L. Kuipers, An irrational sum, Southeast Asian Bull. Math. 1 (1977), 20-21.
- [Lao] V. Laohakosol, A counterexample to Schmidt's conjecture, Southeast Asian Bull. Math. 4 (1980), 48-49.
- [Mah] K. Mahler, On the transcendency of the solutions of a special class of functional equations, Bull. Austral. Math. Soc. 13 (1975), 389-410. Zbl0316.10021
- [Mig1] M. Mignotte, Quelques problèmes d'effectivité en théorie des nombres, Thèse de doctorat, Univ. Paris XIII, 1974.
- [Mig2] M. Mignotte, An application of W. Schmidt's theorem . Transcendental numbers and golden number, Fibonacci Quart. 15 (1977), 15-16. Zbl0353.10025
- [Opp1] A. Oppenheim, The irrationality or rationality of certain infinite series, in: Studies in Pure Math. (presented to Richard Rado), Academic Press, London 1971, 195-201.
- [Opp2] A. Oppenheim, The representation of real numbers by infinite series of rationals, Acta Arith. 21 (1972), 391-398. Zbl0258.10003
- [Sán1] J. Sándor, Some classes of irrational numbers, Studia Univ. Babeş-Bolyai Math. 29 (1984), 3-12.
- [Sán2] J. Sándor, On the irrationality of some alternating series, Studia Univ. Babeş-Bolyai Math. 33 (1988), 8-12.
- [Sch] A. Schinzel, Wac/law Sierpiński's papers on the theory of numbers, Acta Arith. 21 (1972), 7-13.
- [Sie1] W. Sierpiński, O kilku algorytmach dla rozwijania liczb rzeczywistych na szeregi (Sur quelques algorithmes pour développer les nombres réels en séries), C. R. Soc. Sci. Lettres Varsovie Cl. III 4 (1911), 56-77; French transl. in: Oeuvres choisies, tome 1, PWN, Warszawa 1974, 236-254.
- [Sie2] W. Sierpiński, Sur un algorithme pour développer les nombres réels en séries rapidement convergentes, Bull. Internat. Acad. Sci. Lettres Cracovie Sér. A 1911, 113-117.
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.