CONTINUED FRACTION EXPRESSION OF THE MATHIEU SERIES

被引：1
|
作者：
Cao, Xiaodong [1 ]
Tanigawa, Yoshio [2 ]
Zhai, Wenguang [3 ]
机构：
[1] Beijing Inst Petrochem Technol, Dept Math & Phys, Beijing 102617, Peoples R China
[2] Nagoya Univ, Grad Sch Math, Nagoya, Aichi 4648602, Japan
[3] China Univ Min & Technol, Dept Math, Beijing 100083, Peoples R China
来源：
MATHEMATICAL INEQUALITIES & APPLICATIONS | 2016年 / 19卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Continued fraction; Mathieu series; inequality; asymptotic expansion; MULTIPLE-CORRECTION; APPROXIMATION; INEQUALITY;
D O I：
10.7153/mia-19-77
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we represent a continued fraction expression of the Mathieu series by a continued fraction formula of Ramanujan. As applications, we obtain some new bounds for the Mathieu series.
引用
收藏
页码：1039 / 1048
页数：10
相关论文
共 50 条
  • [21] On a continued fraction expansion of the special function exE1(x) and an explicit expression of the continued fraction convergents
    Murabayashi, Naoki
    Yoshida, Hayato
    RAMANUJAN JOURNAL, 2025, 66 (02):
  • [22] Continued-fraction expansion of the Baum-Sweet series
    Mkaouar, M
    BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1995, 123 (03): : 361 - 374
  • [23] CONTINUED FRACTION APPROXIMANTS TO THE BRILLOUIN-WIGNER PERTURBATION SERIES
    YOUNG, RC
    BIEDENHARN, LC
    FEENBERG, E
    PHYSICAL REVIEW, 1957, 106 (06): : 1151 - 1155
  • [24] Continued fraction for formal laurent series and the lattice structure of sequences
    Meidl, W
    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2006, 17 (01) : 29 - 39
  • [25] On a continued fraction of order twelve and new Eisenstein series identities
    Adiga, Chandrashekar
    Liu, Zhi-Guo
    Vanitha, A.
    JOURNAL OF NUMBER THEORY, 2014, 145 : 554 - 571
  • [26] Continued fraction for formal laurent series and the lattice structure of sequences
    Wilfried Meidl
    Applicable Algebra in Engineering, Communication and Computing, 2006, 17 : 29 - 39
  • [27] WALLIS PRODUCT, BROUNCKER CONTINUED-FRACTION, AND LEIBNITZ SERIES
    DUTKA, J
    ARCHIVE FOR HISTORY OF EXACT SCIENCES, 1982, 26 (02) : 115 - 126
  • [28] On Certain Continued Fraction Representations of Poly-basic Series
    Denis, Remy Y.
    Singh, S. N.
    Singh, S. P.
    2008 COMPLEXITY & INTELLIGENCE OF THE ARTIFICIAL & NATURAL COMPLEX SYSTEMS, MEDICAL APPLICATIONS OF THE COMPLEX SYSTEMS, BIOMEDICAL COMPUTING, 2008, : 166 - +
  • [29] On Certain Continued Fraction Representations of Poly-Basic Series
    Denis, Remy Y.
    Singh, S. N.
    Singh, S. P.
    COMPLEXITY IN ARTIFICIAL AND NATURAL SYSTEMS, PROCEEDINGS, 2008, : 290 - 295
  • [30] Some families of Mathieu a-series and alternating Mathieu a-series
    Pogány, TK
    Srivastava, HM
    Tomovski, V
    APPLIED MATHEMATICS AND COMPUTATION, 2006, 173 (01) : 69 - 108
12345