摘要
Following John Wallis, we observe the reciprocal of the integral (The equation is abbreviated), called Wallis function W(p, q). Its beauty is manifested in symmetry, quotient and difference formulas. Next, set p = 1/2 and observe the sequence (The equation is abbreviated). By quotient formula along with induction, we obtain inequalities on (The equation is abbreviated), which then yield the well-known Wallis' infinite product formula on π. Finally, for d∈ N, observing a similar sequence (The equation is abbreviated) as Wallis did for the case d = 2. Exactly the same argument yields an infinite product formula on the integral (The equation is abbreviated) as expected.