cp's OEIS Frontend

A335959 Decimal expansion of s - c, where s = arclength on y = sin(x) from (0,0) to (Pi/4,sqrt(1/2)), and c = arclength on y = cos(x) from (0,1) to (Pi/4,sqrt(1/2)).

%I A335959 #4 Jul 04 2020 01:45:39
%S A335959 2,0,6,0,9,2,1,0,8,2,7,1,2,7,0,1,0,6,5,0,3,3,9,7,7,4,2,7,8,6,1,7,2,1,
%T A335959 2,9,5,4,1,9,9,7,1,9,2,2,3,5,7,4,6,5,0,0,5,8,1,0,4,0,9,2,0,4,4,9,7,6,
%U A335959 7,3,7,1,6,4,0,2,2,4,6,2,9,0,8,3,3,5
%N A335959 Decimal expansion of s - c, where s = arclength on y = sin(x) from (0,0) to (Pi/4,sqrt(1/2)), and c = arclength on y = cos(x) from (0,1) to (Pi/4,sqrt(1/2)).
%e A335959 s/c = 1.24189118251777949328029742670369236529...
%e A335959 c/s = 0.80522352849999684548520974994993752239...
%e A335959 c-s = 0.20609210827127010650339774278617212954...
%t A335959 r1 = NIntegrate[Sqrt[1 + Cos[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
%t A335959 r2 = NIntegrate[Sqrt[1 + Sin[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
%t A335959 r1/r2
%t A335959 r2/r1
%t A335959 r1 - r2
%t A335959 RealDigits[r1/r2][[1]]      (* A335957 *)
%t A335959 RealDigits[r2/r1][[1]]      (* A335958 *)
%t A335959 RealDigits[r1 - r2][[1]]    (* A335959 *)
%Y A335959 Cf. A335928, A335929, A335930, A335931, A335932, A335957, A335958.
%K A335959 nonn,cons
%O A335959 0,1
%A A335959 _Clark Kimberling_, Jul 03 2020