Some hypergeometric summation theorems and reduction formulas via Laplace transform method

In this paper, we obtain analytical solutions of Laplace transform based some generalized class of the hyperbolic integrals in terms of hypergeometric functions 3F2(±1) , 4F3(±1) , 5F4(±1) , 6F5(±1) , 7F6(±1) and 8F7(±1) with suitable convergence conditions, by using some algebraic properties of Pochhammer symbols. In addition, reduction formulas for 4F3(1) , 7F6(−1) and some new summation theorems (not recorded earlier in the literature of hypergeometric functions) for 3F2(−1),6F5(±1) , 7F6(±1) and 8F7(±1) are obtained.