Gosper introduced the functions sinq z and cosq z as q-analogues for the trigonometric functions sin z and cos z respectively. He stated a variety of identities involving these two q-trigonometric functions along with...Gosper introduced the functions sinq z and cosq z as q-analogues for the trigonometric functions sin z and cos z respectively. He stated a variety of identities involving these two q-trigonometric functions along with certain constants denoted by Πqn （n ∈ N）. Gosper noticed that all his formulas on these constants have more than two of the Πqn. So, it is natural to raise the question of establishing identities involving only two of the Πqn. In this paper, our main goal is to give examples of such formulas in only two Πqn.展开更多
文摘Gosper introduced the functions sinq z and cosq z as q-analogues for the trigonometric functions sin z and cos z respectively. He stated a variety of identities involving these two q-trigonometric functions along with certain constants denoted by Πqn （n ∈ N）. Gosper noticed that all his formulas on these constants have more than two of the Πqn. So, it is natural to raise the question of establishing identities involving only two of the Πqn. In this paper, our main goal is to give examples of such formulas in only two Πqn.
