JOURNAL BROWSE
Search
Advanced SearchSearch Tips
APPLICATIONS OF GENERALIZED KUMMER`S SUMMATION THEOREM FOR THE SERIES 2F1
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
APPLICATIONS OF GENERALIZED KUMMER`S SUMMATION THEOREM FOR THE SERIES 2F1
Kim, Yong-Sup; Rathie, Arjun K.;
  PDF(new window)
 Abstract
The aim of this research paper is to establish generalizations of classical Dixon`s theorem for the series , a result due to Bailey involving product of generalized hypergeometric series and certain very interesting summations due to Ramanujan. The results are derived with the help of generalized Kummer`s summation theorem for the series obtained earlier by Lavoie, Grondin, and Rathie.
 Keywords
generalized Kummer`s theorem;generalized Dixon`s theorem;generalized Whipple`s theorem;
 Language
English
 Cited by
1.
ON A NEW CLASS OF SERIES IDENTITIES,;;;;

호남수학학술지, 2015. vol.37. 3, pp.339-352 crossref(new window)
1.
GENERALIZATIONS OF CERTAIN SUMMATION FORMULA DUE TO RAMANUJAN, Honam Mathematical Journal, 2012, 34, 1, 35  crossref(new windwow)
2.
GENERALIZATION OF A RESULT INVOLVING PRODUCT OF GENERALIZED HYPERGEOMETRIC SERIES DUE TO RAMANUJAN, International Journal of Modern Physics: Conference Series, 2013, 22, 679  crossref(new windwow)
3.
ON A NEW CLASS OF SERIES IDENTITIES, Honam Mathematical Journal, 2015, 37, 3, 339  crossref(new windwow)
 References
1.
G. E. Andrews, R. Askey, and R. Roy, Special Functions, Encyclopedia of Mathematics and its Applications, 71. Cambridge University Press, Cambridge, 1999

2.
W. N. Bailey, Product of generalized hypergeometric series, Proc. London Math. Soc. Ser. 2 28 (1928), 242-254 crossref(new window)

3.
W. N. Bailey, Generalized Hypergeometric Series, Cambridge Tracts in Mathematics and Mathematical Physics, No. 32 Stechert-Hafner, Inc., New York 1964

4.
B. C. Berndt, Ramanujan's Notebooks, Part II, Springer-Verlag, New York, 1987

5.
Y. S. Kim and A. K. Rathie, On an extension formulas for the triple hypergeometric series $X_8$ due to Exton, Bull. Korean Math. Soc. 44 (2007), no. 4, 743-751 crossref(new window)

6.
J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalizations of Whipple's theorem on the sum of a $_3F_2$, J. Comput. Appl. Math. 72 (1996), no. 2, 293-300 crossref(new window)

7.
E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960