Research on Quasi-periodic continued fractions in terms of Special functions

特殊函数的拟周期连分式研究

• 批准号: 18540006
• 负责人: KOMATSU Takao
• 金额: $ 2.34万
• 依托单位: Hirosaki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540006/
• 关键词: 整数論; 関数論; 組合せ論; 代数学; Continued fractions; Tasoev continued fractions; Hurwitz continued fractions; Hyprgeometric functions; Diophantine Analysis; Leaping convergents; Hypergeometric functions

Still new types of Hurwitz and Tasoev continued fractions, which belong to quasi-periodic continued fractions, have been found. Several typical relations between quasi-periodic continued fractions and hypergeometric functions, hyperbolic functions, Fibonacci-zeta functions have been discovered. Leaping convergents have been defined from the concept of convergents of quasi-periodic continued fractions. Characteristic properties of leaping convergents have been examined. Leaping convergents have been extensively defined on non-regular continued fractions and on general integer sequences.

还发现了新类型的 Hurwitz 和 Tasoev 连续分数，属于准周期连续分数。已经发现了准周期连分数与超几何函数、双曲函数、Fibonacci-zeta函数之间的几种典型关系。跳跃收敛是根据准周期连续分数收敛的概念定义的。跳跃收敛的特性已经被检验。跳跃收敛已在非常规连分数和一般整数序列上得到了广泛的定义。

项目成果

Powers of Sierpinski numbers base b

谢尔宾斯基数的幂 b 为底

• 发表时间: 2010
• 期刊: INTEGERS
• 作者: Takao Komatsu;V. Laohakosol and P. Ruengsinsub;T. Komatsu and S. H. Holliday;T. Komatsu;T. Komatsu;T. Komatsu;T. Komatsu;C. K. Caldwell and Takao Komatsu
• 通讯作者: C. K. Caldwell and Takao Komatsu

Diophantine approximations of tanh, tan, and linear forms of e in terms of integrals

tanh、tan 和 e 的线性形式的积分形式的丢番图近似

• 发表时间: 2009
• 期刊: Revue Roumaine de Mathematiques Pures et Appliquees 54
• 作者: Carsten Elsner;Takao Komatsu;Iekata Shiokawa;Takao Komatsu;Takao Komatsu;Takao Komatsu;Takao Komatsu
• 通讯作者: Takao Komatsu

More on the continued fractions of e^2

有关 e^2 连分数的更多信息

• 发表时间: 2006
• 期刊: Diophantine Analysis and Related Fields 2006, in honor of lekata Shiokawa, Seminar on Mathematical Sciences 35
• 作者: Carsten Elsner;Takao Komatsu;Iekata Shiokawa;Takao Komatsu
• 通讯作者: Takao Komatsu

A recurrence formula for leaping convergents of non-regular continued fractions

非正则连分数跳跃收敛的递推公式

• 发表时间: 2008
• 期刊: Linear Algebra and its Applications 428
• 作者: Carsten Elsner;Takao Komatsu;Carsten Elsner and Takao Komatsu;小松尚夫 Carsten Elsner
• 通讯作者: 小松尚夫 Carsten Elsner

Continued fraction of e^2 with confluent hypergeometric functions

具有合流超几何函数的 e^2 的连分数

• 发表时间: 2006
• 期刊: Liet. Mat. Rink. 46
• 作者: Carsten Elsner;Takao Komatsu;Iekata Shiokawa;小松尚夫;Takao Komatsu
• 通讯作者: Takao Komatsu