Addition formulas for the ${}_p{F}_p$ and ${}_{p+1}{F}_p$ generalized hypergeometric functions with arbitrary parameters and their Kummer- and Euler-type transformations

We obtain addition formulas for ${}_p{F}_p$ and ${}_{p+1}{F}_p$ generalized hypergeometric functions with general parameters. These are utilized in conjunction with integral representations of these functions to derive Kummer- and Euler-type transformations that express ${}_p{F}_p\left(x\right)$ and ${}_{p+1}{F}_p\left(x\right)$ in the form of sums of ${}_p{F}_p(-x)$ and ${}_{p+1}{F}_p(-x)$ functions, respectively.