Acknowledgement
Supported by : National Research Foundation of Korea
References
- M. Abramowitz, I. A. Stegun (Editors), Handbook of Mathematical Functions with Formulas; Graphs; and Mathematical Tables, Applied Mathematics Series 55, ninth printing, National Bureau of Standards, Washington, D.C., 1972.
- W. N. Bailey, Products of generalized hypergeometric series, Proc. London Math. Soc. 28(1) (1928), 242-250.
- B. C. Berndt, Ramanujan's Notebooks, Part II, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, and Tokyo, 1989.
- J. Choi, Notes on formal manipulations of double series, Commun. Korean Math. Soc. 18(4) (2003), 781-789. https://doi.org/10.4134/CKMS.2003.18.4.781
- P. Chopra and A. K. Rathie, A result closely related to the Ramanujan's result, submitted for publication, 2013.
-
Y. S. Kim and A. K. Rathie, Comment on 'A summation formula for Clausen's series
$_3F_2$ (1) with an application to Goursat's function$_2F_2$ (x)', J. Phys. A: Math. Theor. 41 (2008) 078001 (2pp). https://doi.org/10.1088/1751-8113/41/7/078001 -
A. R. Miller, A summation formula for Clausen's series
$_3F_2$ (1) with an application to Goursat's function$_2F_2$ (x), J. Phys. A: Math. General 16 (2005), 3541-3545. - A. P. Prudnikov, Yu. A. Brychkov and O. I. Marchev, Integrals and Series, More Special Functions, 3, Gordon and Breach Science Publishers, 1990; Translated from the Russian Edition in 1986 by G. G. Gould.
- E. D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
-
A. K. Rathie and R. Paris, An extension of the Euler-type transformation for the
$_3F_2$ series, Far East J. Math. Sci. (FJMS), 27(1) (2007), 43-48. - M. A. Rakha and A. K. Rathie, Extensions of Euler's type II transformation and Saalschutz's theorem, Bull. Korean Math. Soc. 48(1) (2011), 151-156. https://doi.org/10.4134/BKMS.2011.48.1.151
- H. M. Srivastava, J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London, and New York, 2012.
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