In this paper, we investigate the \((d,1)\)-total labelling of generalized Petersen graphs \(P(n,k)\) for \(d\geq 3\). We find that the \((d,1)\)-total number of \(P(n,k)\) with \(d\geq 3\) is \(d+3\) for even \(n\) and odd \(k\) or even \(n\) and \(k=\frac{n}{2}\), and \(d+4\) for all other cases.
By employing Kummer and Thomae transformations, we examine four classes of nonterminating \(_3F_2\)(1)-series with five integer parameters. Several new summation formulae are established in closed form.