Communications of the
Korean Mathematical Society CKMS

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