Generalizations of incomplete elliptic integrals of first and second kinds

Main Article Content

M. I. Qureshi
Kaleem A. Quraishi

Abstract

In this paper, we obtain analytical solutions of incomplete elliptic integrals of first and second kinds. Further, we generalize these incomplete elliptic integrals in the forms of multiple series identities involving bounded multiple sequences.

Article Details

How to Cite
Qureshi, M. I., & Quraishi, K. A. (2012). Generalizations of incomplete elliptic integrals of first and second kinds. Tamkang Journal of Mathematics, 43(4), 595–601. https://doi.org/10.5556/j.tkjm.43.2012.877
Section
Papers
Author Biographies

M. I. Qureshi

Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia(A Central University), New Delhi-110025, India.

Kaleem A. Quraishi, Mewat Engineering College (Wakf)

Mathematics Section,Mewat Engineering College(Wakf), Palla, Nuh,Mewat-122107, Haryana, India.

References

Agarwal, R. P., Resonance of Ramanujan's Mathematics, Vol. I, New Age International(P) Ltd., New Delhi, 1996.

Andrews, G. E. and Berndt, B. C., Ramanujan's Lost Notebook, Part I, Springer-Verlag, New York, 2005.

Berndt, B. C., Ramanujan's Notebooks, Part III, Springer-Verlag, New York, 1991.

Berndt, B. C., Ramanujan's Notebooks, Part V, Springer-Verlag, New York 1998.

Carlson, B. C., Some series and bounds for incomplete elliptic integrals, J. Math. Phys., 40 (1961), 125--134.

Carlson, B. C., Normal elliptic integrals of the first and second kinds, Duke Math. J., 31 (1964), 405--419.

Carlson, B. C., On computing elliptic integrals and functions, J. Math. Phys., 44 (1965), 36--51.

Carlson, B. C., Computing Elliptic Integrals by Duplication, Numerische Mathematik,33(1) (1979).

Carlson, B. C., Numerical computation of real or complex elliptic integrals, Numerical Algorithms, 10(1)(1995), 13--26.

Olver, F. W. J., Lozier, D. W., Boisvert, R. F. and Clark, C. W., NIST Handbook of Mathematical Functions, Cambridge University Press, 2010.

Ramanujan, S., Notebooks of Srinivasa Ramanujan, Vol. I, Tata Institute of Fundamental Research, Bombay, 1957; Reprinted by Narosa Publishing House, New Delhi, 1984.

Ramanujan, S., Notebooks of Srinivasa Ramanujan, Vol. II, Tata Institute of Fundamental Research, Bombay, 1957; Reprinted by Narosa Publishing House, New Delhi, 1984.

Ramanujan, S., The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988.

Srivastava, H. M. and Karlsson, Per W., Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Ltd., Chichester, Brisbane, U. K.) John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.