Value of π

A pretty series revisited

“…Of course the real advantage of the formulation presented leading to ( 4) is it provides one with a means for finding a closed-form expression for the Maclaurin series given in (2), on the condition one is able to evaluate the integral appearing in (4). That this can indeed be done we now show.…”

“…The sum is no doubt intriguing and, interestingly, its proposer is the same Ferguson who, a decade earlier, had found an error in the 528th decimal place of the monumental 707 decimal place calculation of completed by William Shanks in 1873 (see [2,3]).…”