New analytic continuations for the Appell $F_4$ series from quadratic transformations of the Gauss ${}_2{F}_1$ function

B. Ananthanarayan, Samuel Friot, Shayan Ghosh +1

We present new analytic continuation formulas for the Appell $F_4(a,b;c,d;x,y)$ double hypergeometric series where $d=a-b+1$, which allows quadratic transformations of the Gauss ${…