East Asian mathematical journal

  • 제33권3호
  • /
  • Pages.291-293
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  • 2017
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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TWO IDENTITIES INVOLVING THETA FUNCTIONS

  • 투고 : 2017.03.17
  • 심사 : 2017.04.12
  • 발행 : 2017.05.31
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초록

We aim to present two identities which reveal certain interesting relationships among three fundamental theta functions arising from the Jacobi's triple product in an elementary way.

키워드

참고문헌

  1. M. P. Chaudhary, On q-product identities, Pacific J. Appl. Math. 5(2) (2013), 123-129.
  2. M. P. Chaudhary and J. Choi, Note on modular relations for Roger Ramanujan type identities and representation for Jacobi identities, East Asian Math. J. 31(5) (2015), 659-665. https://doi.org/10.7858/eamj.2015.046
  3. M. P. Chaudhary and G. A. Salilew, Elementary proof for theta function identities, submitted, 2017.
  4. Z. Cao, Integer matrix exact covering sytems and product identities for theta functions, Inter. Math. Res. Notices 19 (2011), 4471-4514.
  5. S. Cooper, The quinntuble product identity, Int. J. Number Theory 2(1) (2006), 115-161. https://doi.org/10.1142/S1793042106000401
  6. M.D. Hirschorn, A simple proof of an identity of Ramanujan, J. Austral. Math. Soc. Ser. A 44(1)(1988), 42-45. https://doi.org/10.1017/S1446788700031359
  7. G. J. Jacobi, Fundamental Nova Theoriae Functionum Ellipticarum, Sumptibus Fratrum Borntrger, Regiomonti, 1829.
  8. H. Schroter, De Aequationibus Modularibus, Disserrtatio Inaugurolis, Albertino, Litterarum University, Regiomonti, 1854.
  9. J. L. C. Villacorto, Problems on theta function identities.
  10. J. L. C. Villacorto and M. P. Chaudhary, On Certain theta function identities, submitted, (2017).

피인용 문헌

  1. A Family of Theta-Function Identities Related to Jacobi’s Triple-Product Identity vol.27, pp.1, 2020, https://doi.org/10.1134/s1061920820010148