Bisection Series Approach for Exotic 3F2(1)-Series

By employing the bisection series approach, two classes of nonterminating F-3(2)(1)-series are examined. Several new summation formulae are established in closed form through the summation formulae of Gauss and Kummer for the F-2(1)(+/- 1)-series. They are expressed in terms of well-known functions such as pi, Euler-Gamma, and logarithmic functions, which can be used in physics and applied sciences for numerical and theoretical analysis.