• Journal of the Korean Mathematical Society
• /
• v.48 no.1
• /
• pp.169-178
• /
• 2011

In this paper, we find character analogues of infinite series identities which come from a certain modular transformation formula given by B. C. Berndt.

• Journal of the Chungcheong Mathematical Society
• /
• v.35 no.4
• /
• pp.277-295
• /
• 2022

The author proved a modular transformation formula for a function related to generalized non-holomorphic Eisenstein series and, using this formula, established a lot of infinite series identities. In this paper, we find more generalized series relations which contain the author's previous work.

• Honam Mathematical Journal
• /
• v.35 no.3
• /
• pp.507-513
• /
• 2013

In this paper, we compute transformation formulae for generalized non-holomorphic Eisenstein series.

• Honam Mathematical Journal
• /
• v.43 no.2
• /
• pp.221-237
• /
• 2021

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.

• Honam Mathematical Journal
• /
• v.36 no.4
• /
• pp.895-899
• /
• 2014

In this paper, we consider generalized two variable Eisenstein series. We give analytic continuation and prove modular transformation formulae for them.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.4
• /
• pp.421-440
• /
• 2019

We establish a few class of infinite series identities from modular transformation formulas for certain series which originally come from generalized non-holomorphic Eisenstein series.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.3
• /
• pp.481-502
• /
• 2011

B. C. Berndt [4, 5] evaluated several classes of infinite series and established many relations between various infinite series. In this paper, continuing his work, we derive new relations between infinite series.

• Journal of the Chungcheong Mathematical Society
• /
• v.34 no.2
• /
• pp.139-155
• /
• 2021

Using a modular transformation formula for a class of functions related to generalized non-holomorphic Eisenstein series, we find a new class of infinite series about identities, some of which include generalized formulae of several Berndt's results.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.2
• /
• pp.299-312
• /
• 2012

In 1970s, B. C. Berndt proved a transformation formula for a large class of functions that includes the classical Dedekind eta function. From this formula, he evaluated several classes of infinite series and found a lot of interesting infinite series identities. In this paper, using his formula, we find new infinite series identities.

• Honam Mathematical Journal
• /
• v.34 no.3
• /
• pp.391-401
• /
• 2012

B. C. Berndt has found a transformation formula for a large class of functions, which comes from a transformation formula for a more general class of Eisenstein series. In this paper, using his formula which is 'twisted' by change of variables, we find a class of infinite series identities.