Generalized Watsonʹs summation formula for 3F2(1)

A summation formula is given for 3F2(a, b, c; 12(a + b + i + 1), 2c + j; 1) with fixed j and arbitrary i(i,j∈Z). This result generalizes the classical Watsonʹs theorem which deals with the case i = j = 0. ions to the cases of 3F2(a, 1 + i + j − a,c;e, 1 + i + 2c − e; 1), and 3F2(a, b, c; 1 + i + a − b, 1 + i + j + a − c; 1) are given. Notice that the case i = j = 0 corresponds to the classical theorems due to Whipple and Dixon, respectively.