On the bilateral series \({}_5\psi_5\) (Q2473812)

Two transformation formulas are derived for a bilateral basic hypergeometric series \({}_5\psi_5\). One in terms of a \({}_8\phi_7\) and a \({}_7\phi_6\) basic hypergeometric series and the other one in terms of a \({}_8\phi_7\) and a \({}_6\phi_5\) basic hypergeometric series. Both are obtained from Bailey's transformation formula for a very-well-poised \({}_8\phi_7\) basic hypergeometric series. Some special cases are also discussed. Among these are results for a \({}_4\psi_4\) and a \({}_3\psi_3\) bilateral basic hypergeometric series.