A theorem on irrationality of infinite series and applications
C. Badea
Acta Arithmetica, Tome 64 (1993), p. 313-323 / Harvested from The Polish Digital Mathematics Library
Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:206523
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     title = {A theorem on irrationality of infinite series and applications},
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     volume = {64},
     year = {1993},
     pages = {313-323},
     zbl = {0770.11036},
     language = {en},
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C. Badea. A theorem on irrationality of infinite series and applications. Acta Arithmetica, Tome 64 (1993) pp. 313-323. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav63i4p313bwm/

[000] [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. | Zbl 0682.10025

[001] [AnJ2] R. André-Jeannin, A note on the irrationality of certain Lucas infinite series, Fibonacci Quart., to appear.

[002] [Bad] C. Badea, The irrationality of certain infinite series, Glasgow Math. J. 29 (1987), 221-228. | Zbl 0629.10027

[003] [BuP] P. Bundschuh und A. Pethö, Zur Transzendenz gewisser Reihen, Monatsh. Math. 104 (1987), 199-223. | Zbl 0601.10025

[004] [Cuc] R. Cuculière, Problem E 2922, Amer. Math. Monthly 89 (1982), 63; solution, Amer. Math. Monthly 91 (1984), 435.

[005] [DaS] J. L. Davison and J. O. Shallit, Continued fractions for some alternating series, Monatsh. Math. 111 (1991), 119-126. | Zbl 0719.11038

[006] [Erd] P. Erdős, Some problems and results on the irrationality of the sum of infinite series, J. Math. Sci. 10 (1975), 1-7.

[007] [ErG] P. Erdős and R. L. Graham, Old and New Problems and Results in Combinatorial Number Theory, Monograph. Enseign. Math. 28, Genève 1980.

[008] [ErS] P. Erdős and E. G. Straus, On the irrationality of certain Ahmes series, J. Indian Math. Soc. 27 (1963), 129-133. | Zbl 0131.04902

[009] [Gal] J. Galambos, The Representation of Real Numbers by Infinite Series, Lecture Notes in Math. 502, Springer, 1976.

[010] [Han] D. Hanson, On the product of the primes, Canad. Math. Bull. 15 (1975), 33-37. | Zbl 0231.10008

[011] [Kui] L. Kuipers, An irrational sum, Southeast Asian Bull. Math. 1 (1977), 20-21.

[012] [Lao] V. Laohakosol, A counterexample to Schmidt's conjecture, Southeast Asian Bull. Math. 4 (1980), 48-49.

[013] [Mah] K. Mahler, On the transcendency of the solutions of a special class of functional equations, Bull. Austral. Math. Soc. 13 (1975), 389-410. | Zbl 0316.10021

[014] [Mig1] M. Mignotte, Quelques problèmes d'effectivité en théorie des nombres, Thèse de doctorat, Univ. Paris XIII, 1974.

[015] [Mig2] M. Mignotte, An application of W. Schmidt's theorem . Transcendental numbers and golden number, Fibonacci Quart. 15 (1977), 15-16. | Zbl 0353.10025

[016] [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.

[017] [Opp2] A. Oppenheim, The representation of real numbers by infinite series of rationals, Acta Arith. 21 (1972), 391-398. | Zbl 0258.10003

[018] [Sán1] J. Sándor, Some classes of irrational numbers, Studia Univ. Babeş-Bolyai Math. 29 (1984), 3-12.

[019] [Sán2] J. Sándor, On the irrationality of some alternating series, Studia Univ. Babeş-Bolyai Math. 33 (1988), 8-12.

[020] [Sch] A. Schinzel, Wac/law Sierpiński's papers on the theory of numbers, Acta Arith. 21 (1972), 7-13.

[021] [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.

[022] [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.