An improvement of the two-line algorithm for proving q-hypergeometric identities Original Research Article

Yen (J. Math. Anal. Appl. 213 (1996) 1) gives a two-line algorithm to show that q-hypergeometric identities∑k F(n,k)=1, n⩾n0can be proved by checking that they are correct for n∈{n0,n0+1,…,n1}. Here we generalize Sister Celineʹs technique and give a specific formula for n1, bounded above by a polynomial of degree of 9 in the parameters of F(n,k). This n1 is much smaller than the estimate of Yen (1996), as a polynomial of degree of 24 in the parameters of F(n,k).