Modular identities and dissections of continued fractions of order thirty-two

被引：0
作者：
Jubaraj Chetry
Nipen Saikia
机构：
[1] Paschim Dhemaji College,Department of Mathematics
[2] Rajiv Gandhi University,Department of Mathematics
来源：
São Paulo Journal of Mathematical Sciences | 2023年 / 17卷
关键词：
Continued fraction; Theta-functions; Dissections formulas; 33D15; 40A15; 11A55; 30B70;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we derive four continued fractions of order 32 as special cases of a general continued fraction identity recorded by Ramanujan. We prove theta-function representations and establish a modular relation connecting the four continued fractions. We also prove 2-, 4-, 8-, and 16-dissections for a continued fraction and show that the sign of the coefficients in the power series expansion of a continued fraction and its reciprocal are periodic with period 32. The results are analogous to those of the famous Rogers-Ramanujan continued fraction.
引用
收藏
页码：701 / 719
页数：18
相关论文
共 5 条
  • [1] Hirschhorn MD(1998)On the expanssion of continued fraction Ramanujan J. 2 521-527
  • [2] Lin BLS(2013)On the expansion of continued fraction of order twelve Int. J. Number Thy. 9 2019-2031
  • [3] Richmond B(1978)The Taylor coefficients of certain infinite products Acta Sci. Math. 40 347-369
  • [4] Szekeres G(2017)On the modular relations and dissections for a continued fraction of order sixteen Palestine J. Math. 6 119-132
  • [5] Surekha MS(undefined)undefined undefined undefined undefined-undefined
1