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

页码：701 / 719

页数：18

共 5 条

[1]

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[2]

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[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]

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