논문KCI 등재
SOME INFINITE SERIES IDENTITIES
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
B.C. Berndt has established many relations between various infinite series using a transformation formula for a large class of functions, which comes from a more general class of Eisenstein series. In this paper, continuing his study, we find some infinite series identities.
Abstract
B.C. Berndt has established many relations between various infinite series using a transformation formula for a large class of functions, which comes from a more general class of Eisenstein series. In this paper, continuing his study, we find some infinite series identities.
참고문헌 (10)
- M. Abramowitz, "Handbook of mathematical functions", New York, ~ (1965)
- B.C. Berndt, "Generalized Dedekind eta-functions and generalized Dedekind sums", Trans. Amer. Math. Soc, 178, pp.495~508 (1973)
- B.C. Berndt, "Modular transformations and generalizations of several formulae of Ramanujan", Rocky mountain J. Math, 7(1), pp.147~189 (1977)
- B.C. Berndt, "Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan", J. Reine Angew. Math, 304, pp.332~365 (1978)
- J. Lagrange, "Une formule sommatoire et ses applications", Bull. Sci. Math, 84(2), pp.105~110 (1960)
- S. Ramanujan, "Notebooks of Srinivasa Ramanujan" (1957), Tata Institute of Fundamental Research
- O. Schlomilch, "Ueber einige unendliche Reichen", Berichte uber die Verh. d. Konige Sachsischen Gesell. Wiss. zu Leipzig, 29, pp.101~105 (1877)
- O. Schlomilch, "Compendium der hoheren Analysis, Zweiter Band, 4th ed" (1895), Friedrich Vieweg und Sohn
- G.N. Watson, "Theorems stated by Ramanujan II", J. Lond. Math. Soc, 3, pp.216~225 (1928)
- E.T. Whittaker, "A course in modern analysis, 4th ed" (1990), England
관련 논문AI추천
CHARACTER ANALOGUES OF INFINITE SERIES FROM A CERTAIN MODULAR TRANSFORMATION FORMULA임성근대한수학회 · 대한수학회지2011 · 제48권 제1호Identities about infinite series containing hyperbolic functions and trigonometric functions임성근강원경기수학회 · 한국수학논문집2011 · 제19권 제4호Character analogues of infinite series identities related to generalized non-holomorphic Eisenstein series임성근강원경기수학회 · 한국수학논문집2022 · 제30권 제1호Analytic continuation of generalized non-holomorphic Eisenstein series임성근강원경기수학회 · 한국수학논문집2013 · 제21권 제3호Identities about level 2 Eisenstein seriesCe Xu대한수학회 · 대한수학회논문집2020 · 제35권 제1호On some identities of Ramanujan found in his lost notebookD.D. Somashekara, D. Mamta장전수학회 · Advanced Studies in Contemporary Mathematics2008 · 제16권 제2호
이 간행물의 다른 논문 (17건)
KRONECKER FUNCTION RINGS AND PRUFER-LIKE DOMAINS장규환pp. 371-379SET-VALUED CHOQUET-PETTIS INTEGRALS박춘기pp. 381-393DIAMETER OF THE DIRECT PRODUCT OF WIELANDT GRAPH김수연, 송병철pp. 395-402EVERY LINK IS A BOUNDARY OF A COMPLETE BIPARTITE GRAPH K(2,n)김동석, 전상민, 장용준pp. 403-414WEAK PROPERTY (Bk)이종성, 조규근pp. 415-422