A theorem on irrationality of infinite series and applications

C. Badea

Acta Arithmetica (1993)

  • Volume: 63, Issue: 4, page 313-323
  • ISSN: 0065-1036

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C. 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

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  2. [AnJ2] R. André-Jeannin, A note on the irrationality of certain Lucas infinite series, Fibonacci Quart., to appear. 
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  12. [Kui] L. Kuipers, An irrational sum, Southeast Asian Bull. Math. 1 (1977), 20-21. 
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  14. [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
  15. [Mig1] M. Mignotte, Quelques problèmes d'effectivité en théorie des nombres, Thèse de doctorat, Univ. Paris XIII, 1974. 
  16. [Mig2] M. Mignotte, An application of W. Schmidt's theorem . Transcendental numbers and golden number, Fibonacci Quart. 15 (1977), 15-16. Zbl0353.10025
  17. [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. 
  18. [Opp2] A. Oppenheim, The representation of real numbers by infinite series of rationals, Acta Arith. 21 (1972), 391-398. Zbl0258.10003
  19. [Sán1] J. Sándor, Some classes of irrational numbers, Studia Univ. Babeş-Bolyai Math. 29 (1984), 3-12. 
  20. [Sán2] J. Sándor, On the irrationality of some alternating series, Studia Univ. Babeş-Bolyai Math. 33 (1988), 8-12. 
  21. [Sch] A. Schinzel, Wac/law Sierpiński's papers on the theory of numbers, Acta Arith. 21 (1972), 7-13. 
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  23. [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. 

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