DOI QR코드

DOI QR Code

A CLASS OF INFINITE SERIES FROM GENERALIZED EISENSTEIN SERIES

  • Received : 2012.06.19
  • Accepted : 2012.07.18
  • Published : 2012.09.25

Abstract

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.

Keywords

References

  1. M. Abramowitz and I. A. Stegun, editor, Handbook of mathematical functions, New York 1965.
  2. B. C. Berndt, Modular transformations and generalizations of several formulae of Ramanujan, The Rocky mountain J. Math. 7, no 1 (1977), 147-189. https://doi.org/10.1216/RMJ-1977-7-1-147
  3. B. C. Berndt, Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan, J. Reine. Angew. Math. 304 (1978), 332-365.
  4. J. Gilles, Problem 5952, Solution by B. C. Berndt, Amer. Math. Math. Monthly 82 (1975), 679-681. https://doi.org/10.2307/2319722
  5. S. L. Malurkar, On the application of Herr Mellin's integrals to some series, J. Indian Math. Soc. 16 (1925-1926), 130-138.
  6. T. S. Nanjundiah, Certain summations due to Ramanujan, and their generalizations, Proc. Indian Acad. Sci. Sect. A 34 (1951), 215-228.
  7. S. Ramanujan, Notebooks of Srinivasa Ramanujan (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.