Some Properties on the Error-Sum Function of Alternating Sylvester Series
ABSTRACT
The error-sum function of alternating Sylvester series is introduced. Some elementary properties of this function are studied. Also, the hausdorff dimension of the graph of such function is determined.
The error-sum function of alternating Sylvester series is introduced. Some elementary properties of this function are studied. Also, the hausdorff dimension of the graph of such function is determined.
Cite this paper
H. Jing and L. Shen, "Some Properties on the Error-Sum Function of Alternating Sylvester Series," Advances in Pure Mathematics, Vol. 2 No. 6, 2012, pp. 459-463. doi: 10.4236/apm.2012.26070.
H. Jing and L. Shen, "Some Properties on the Error-Sum Function of Alternating Sylvester Series," Advances in Pure Mathematics, Vol. 2 No. 6, 2012, pp. 459-463. doi: 10.4236/apm.2012.26070.
References
[1] S. Kalpazidou, A. Knopfmacher and J. Knopfmacher, “Lüroth-Type Alternating Series Representations for Real Numbers,” Acta Arithmetica, Vol. 55, No. 4, 1990, pp. 311-322. [2] K. H. Indiekofer, A. Knopfmacher and J. Knopfmacher, “Alternating Balkema-Oppenheim Expansions of Real Numbers,” Bulletin de la Société Mathématique, Vol. B44, 1992, pp. 17-28. [3] S. Kalpazidou, A. Knopfmacher and J. Knopfmacher, “Metric Properties of Alternating Lüroth Series,” Potugaliae Mathematica, Vol. 48, No. 3, 1991, pp. 319-325. [4] J. Barrionuevo, M. Burton-Robert, Dajani-Karma and C. Kraaikamp, “Ergodic Properties of Generalized Lüroth Series,” Acta Arithmetica, Vol. 74, No. 4, 1996, pp. 311-327. [5] K. Dajani and C. Kraaikamp, “On Approximation by Lüroth Series,” Journal de Théorie des Nombres de Bordeaux, Vol. 8, No. 2, 1996, pp. 331-346. doi:10.5802/jtnb.172 [6] K. J. Falconer, “Fractal Geometry, Mathematical Foundations and Applications,” Wiley, Hoboken, 1990. [7] K. J. Falconer, “Techniques in Fractal Geometry,” Wiley, Hoboken, 1997. [8] J. Galambos, “Reprentations of Real Numbers by Infinite Series,” Lecture Notes in Math, Springer, Berlin, 1976. [9] L. M. Shen and J. Wu, “On the Error-Sum Function of Lüroth Series,” Mathematics Analysis and Applications, Vol. 329, No. 2, 2007, pp. 1440-1445. [10] L. M. Shen, C. Ma and J. H. Zhang, “On the Error-Sum Function of Alternating Lüroth Series,” Analysis in Theory and Applications, Vol. 22, No. 3, 2006, pp. 223-232. doi:10.1007/s10496-006-0223-x [11] T. Sálat and S. Znám, “On the Sums of Prime Powers,” Acta Universitatis Palackianae Olomucensis of Mathematica, Vol. 21, 1968, pp. 21-25.
[1] S. Kalpazidou, A. Knopfmacher and J. Knopfmacher, “Lüroth-Type Alternating Series Representations for Real Numbers,” Acta Arithmetica, Vol. 55, No. 4, 1990, pp. 311-322. [2] K. H. Indiekofer, A. Knopfmacher and J. Knopfmacher, “Alternating Balkema-Oppenheim Expansions of Real Numbers,” Bulletin de la Société Mathématique, Vol. B44, 1992, pp. 17-28. [3] S. Kalpazidou, A. Knopfmacher and J. Knopfmacher, “Metric Properties of Alternating Lüroth Series,” Potugaliae Mathematica, Vol. 48, No. 3, 1991, pp. 319-325. [4] J. Barrionuevo, M. Burton-Robert, Dajani-Karma and C. Kraaikamp, “Ergodic Properties of Generalized Lüroth Series,” Acta Arithmetica, Vol. 74, No. 4, 1996, pp. 311-327. [5] K. Dajani and C. Kraaikamp, “On Approximation by Lüroth Series,” Journal de Théorie des Nombres de Bordeaux, Vol. 8, No. 2, 1996, pp. 331-346. doi:10.5802/jtnb.172 [6] K. J. Falconer, “Fractal Geometry, Mathematical Foundations and Applications,” Wiley, Hoboken, 1990. [7] K. J. Falconer, “Techniques in Fractal Geometry,” Wiley, Hoboken, 1997. [8] J. Galambos, “Reprentations of Real Numbers by Infinite Series,” Lecture Notes in Math, Springer, Berlin, 1976. [9] L. M. Shen and J. Wu, “On the Error-Sum Function of Lüroth Series,” Mathematics Analysis and Applications, Vol. 329, No. 2, 2007, pp. 1440-1445. [10] L. M. Shen, C. Ma and J. H. Zhang, “On the Error-Sum Function of Alternating Lüroth Series,” Analysis in Theory and Applications, Vol. 22, No. 3, 2006, pp. 223-232. doi:10.1007/s10496-006-0223-x [11] T. Sálat and S. Znám, “On the Sums of Prime Powers,” Acta Universitatis Palackianae Olomucensis of Mathematica, Vol. 21, 1968, pp. 21-25.