Communications of the
Korean Mathematical Society CKMS

In 1812, Gauss obtained fifteen contiguous functions relations. Later on, 1847, Henie gave their q-analogue. Recently, good progress has been done in finding more contiguous functions relations by employing results due to Gauss. In 1999, Cho et al. have obtained 24 new and interesting contiguous functions relations with the help of Gauss's 15 contiguous relations. In fact, such type of 72 relations exists and therefore the rest $48$ contiguous functions relations have very recently been obtained by Rakha et al.. Thus, the paper is in continuation of the paper \cite{Rakha} published in Computer \& Mathematics with Applications {\bf 61} (2011), 620--629. In this paper, first we obtained 15 q-contiguous functions relations due to Henie by following a different method and then with the help of these 15 q-contiguous functions relations, we obtain 72 new and interesting q-contiguous functions relations. These q-contiguous functions relations have wide applications.

Keywords: basic hypergeometric series, q-contiguous functions relations, Gauss's contiguous functions relations

MSC numbers: 33C05, 33D15