Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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MODULAR TRANSFORMATION FORMULAE COMING FROM GENERALIZED NON-HOLOMORPHIC EISENSTEIN SERIES AND INFINITE SERIES IDENTITIES

  • Lim, Sung Geun (Department of Mathematics Education, Mokwon University)
  • Received : 2020.12.24
  • Accepted : 2021.03.18
  • Published : 2021.06.25
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Abstract

B. C. Berndt has found modular transformation formulae for a large class of functions coming from generalized Eisenstein series. Using those formulae, he established a lot of infinite series identities, some of which explain many infinite series identities given by Ramanujan. Continuing his work, the author proved a lot of new infinite series identities. Moreover, recently the author found transformation formulae for a class of functions coming from generalized non-holomorphic Eisenstein series. In this paper, using those formulae, we evaluate a few new infinite series identities which generalize the author's previous results.

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Acknowledgement

This study was supported by research year of Mokwon University in 2020.

References

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