Clausen's Series 3F2(1) with Integral Parameter Differences

Ebisu and Iwassaki proved that there are three-term relations for F-3(2)(1) with a group symmetry of order 72. In this paper, we apply some specific three-term relations for F-3(2)(1) to partially answer the open problem raised by Miller and Paris in 2012. Given a known value F-3(2)((a,b,x),(c,x+1),1), if f-x is an integer, then we construct an algorithm to obtain F-3(2)((a,b,f),(c,f+n),1) in an explicit closed form, where n is a positive integer and a,b,c and f are arbitrary complex numbers. We also extend our results to evaluate some specific forms of( p+1)F(p)(1), for any positive integer p & GE;2.</p>