Besides “Wallis’ Pi“, there is another remarkable expression for the number as an infinite product. We derive it as follows:
From the trigonometric identity
,
we have
.
That is,
Dividing both sides by yields
or,
.
It follows that since ,
;
i.e.,
Let
(1) becomes
We know
Applying the half-angle formula
gives
Hence,
We compute the value of according to (3):

Fig. 1
Exercise-1 Compute from (1) by letting