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 A new proof of Saalsch\"{u}tz's theorem for the series ${}_3F_2(1)$ and its contiguous results with applications Commun. Korean Math. Soc. 2012 Vol. 27, No. 1, 129-135 https://doi.org/10.4134/CKMS.2012.27.1.129Printed March 1, 2012 Yong Sup Kim and Arjun Kumar Rathie Wonkwang University, Vedant College of Engineering and Technology, Tulsi Abstract : The aim of this paper is to establish the well-known and very useful classical Saalsch\"{u}tz's theorem for the series ${}_3F_2(1)$ by following a different method. In addition to this, two summation formulas closely related to the Saalsch\"{u}tz's theorem have also been obtained. The results established in this paper are further utilized to show how one can obtain certain known and useful hypergeometric identities for the series $_{3}F_{2}(1)$ and $_{4}F_{3}(1)$ already available in the literature. Keywords : Saalsch\"utz's theorem, integral transformation, Kummer's transformation, Vandemonde's theorem. MSC numbers : 33C05, 33C20 Downloads: Full-text PDF

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