Mathematics in Ancient and Medieval India c8.s3.42

c8.s3.42

Substituting (6) in (8), we can calculate a₁, a₂_2p. We verify that a₂ = a₄ = = a_2p = 0. Any function of the type (6) can be taken as f (x), after calculating a₁, a₂_2p in this way, the further coefficients a_2p+1 etc.. being chosen arbitrarily in a convenient manner. We then use ( 4 ) and ( 5 ) to get a series for π in which $U_n = 0 ( 1/(n2p+1) ) .$