LAUSR

Abstract An asymptotic approximation of Wallis' sequence m ↦ W m : = ∏ k = 1 m 4 k 2 4 k 2 − 1 is presented as W m = m π 2 m + 1 exp ⁡ ( 2 σ q ( m ) ) ⋅ exp ⁡ ( r q ( m ) ) , where σ q ( x ) : = ∑ i = 1 ⌊ q / 2 ⌋ ( 1 − 4 − i ) B 2 i i ( 2 i − 1 ) ⋅ x 2 i − 1 ( B k  are the Bernoulli coefficients ) , and where | r q ( m ) | r q ⁎ ( m ) : = 2 π ( q − 2 ) ! 3 ( 2 m π ) q − 1 ,  for any integers  m ≥ 1  and  q ≥ 2 . Parameters m and q control the error factor exp ⁡ ( r q ( m ) ) .