Schlomilch Series

被引：0
|
作者：
Baricz, Arpad [1 ,2 ]
Masirevic, Dragana Jankov [3 ]
Pogany, Tibor K. [4 ]
机构：
[1] Obuda Univ, Inst Appl Math, John Von Neumann Fac Informat, Budapest, Hungary
[2] Babes Bolyai Univ, Dept Econ, Cluj Napoca, Romania
[3] Josip Juraj Strossmayer Univ Osijek, Dept Math, Osijek, Croatia
[4] Univ Rijeka, Fac Maritime Studies, Rijeka, Croatia
来源：
SERIES OF BESSEL AND KUMMER-TYPE FUNCTIONS | 2017年 / 2207卷
关键词：
D O I：
10.1007/978-3-319-74350-9_4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This chapter is devoted to the study of integral representations of Schlomilch series built by Bessel functions of the first kind and modified Bessel functions of the second kind. Closed expressions for some special Schlmilch series together with their connection to Mathieu series are also investigated. The chapter ends with an integral representation formula for number theoretical summation by Popov, which also covers the theta- transform identity coming from functional equation for the Epstein Zeta function.
引用
收藏
页码：113 / 138
页数：26
相关论文
共 50 条
  • [1] On the theory of Schlomilch series
    Cooke, RG
    [J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1928, 28 : 207 - 241
  • [2] M-DIMENSIONAL SCHLOMILCH SERIES
    MILLER, AR
    [J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1995, 38 (03): : 347 - 351
  • [3] Schlomilch series and grating sums
    McPhedran, RC
    Nicorovici, NA
    Botten, LC
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2005, 38 (39): : 8353 - 8366
  • [4] Summation of a Schlomilch type series
    Asatryan, A. A.
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2015, 471 (2183):
  • [5] ON EXTENDED MULTIDIMENSIONAL SCHLOMILCH SERIES
    ALLEN, S
    PATHRIA, RK
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1995, 28 (20): : 5757 - 5765
  • [6] On the summation of Schlomilch's series
    Trickovic, Slobodan B.
    Stankovic, Miomir S.
    Vidanovic, Mirjana V.
    [J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2020, 31 (05) : 339 - 367
  • [7] On the expansion of any function into a series of Schlomilch
    Mindlin, JA
    [J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES DE L URSS, 1936, 10 : 151 - 153
  • [8] On Schlomilch series associated with certain Dirichlet series
    Carletti, E
    Bragadin, GM
    [J]. MANUSCRIPTA MATHEMATICA, 1998, 97 (01) : 117 - 133
  • [9] Summation of some trigonometric and Schlomilch series
    Stankovic, MS
    Vidanovic, MV
    Trickovic, SB
    [J]. JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2003, 5 (03) : 313 - 331
  • [10] Efficient computation of Schlomilch-type series
    Linton, CM
    Barnett, DC
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2004, 460 (2044): : 1177 - 1191
12345