• Choi, June-Sang (Department of Mathematics, College of Natural Sciences, Dongguk University) ;
  • H.M.Srivastava (Department of Mathematics and Statistics, University of Victoria) ;
  • Kim, Yong-Sup (Department of Mathematics, College of Natural Sciences, Wonkwang University)
  • Published : 2001.04.01


The main object of this paper is first to give tow contiguous analogues of a well-known hypergeometric summation formula for $_2$F$_1$(1/2). We then apply each of these analogues with a view to evaluating the sums of several classes of series in terms of Psi(or Digamma) and the Zeta functions. Relevant connections of the series identities presented here with those given elsewhere are also pointed out.


  1. J. Math. Anal. Appl. v.159 A certain family of infinite series associated with Digamma functions B. N. Al-Saqabi;S. L. Kalla;H. M. Srivastava
  2. J, Math. Anal. Appl. v.190 Fractional calculus and the sums of certain families of infinite series J. Aular de Duran;S. L. Kalla;H. M. Srivastava,
  3. Proc. Amer. Math. Soc. v.123 On an intriguing integaral and some series related to ζ(4) D. Borwein;J. M. Borwein
  4. Indian J. Pure Appl. Math. v.23 Evaluation of some ingifite series J. Choi;T. Y. Seo
  5. Monatsh. Math. v.127 Certain classes of infinite series J. Choi;H. M. Srivastava
  6. Soochow J. Math. v.25 Some families of infinite series J. Choi;H. M. Srivastava;T. Y. Seo;A. K. Rathie
  7. Advanced combinatorics: The Art of Finite and Infinite Expansions L. Comtet;J. W. Nienhuys(Tr.)
  8. The Summation of Series H. T. Davis
  9. Tables of Intergrals, Series and Products L. S. Gradshteyn;I. M. Ryzhik;A. Jeffrey(ed.)
  10. A Table of Weries and Products E. R. Hansen
  11. J. Reine Angew. Math. v.15 Uber die hypergeometrische Reihe... E. E. Kummer
  12. Indian J. Math. v.34 Generalizations of Watson's theorem on the sun of a ₃F2 J. L. Lavoie;F. Grondin;A. K. Rathie
  13. Problems and Theorems in Analysis v.1 G. Polya;G. Szego;D. Aeppli(tr.)
  14. The Macmillan Company Special Functions E. D. Rainville
  15. Matematiche(Catania) v.50 On Kummer's second theorem involving product of generalized hypergeometric series A. K. Rathie;V. Nagar
  16. Trans. Amer. Math. Soc. v.347 Remarks on some integrals and series involving the Stirling numbers and (n) Li-Chien Shen
  17. A Treatise on Generating Functions H, M. Srivasrava;H. L. Manocha;
  18. A Course of Modern Analysis, E. T. Whittaker;G. N. Watson