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A096955 Denominators of rational approximation to Pi/4 from Machins's formula. 5

%I #20 Jan 03 2024 17:17:40

%S 1195,1706489875,12184551018734375,24359780855939418203125,

%T 104359128170408663038552734375,1639301884061026141391921953564453125,

%U 30432532948821209122295591520605416259765625

%N Denominators of rational approximation to Pi/4 from Machins's formula.

%C Machin's formula: Pi/4 = 4*arctan(1/5) - arctan(1/239).

%C Numerators are given in A096954.

%D W. Walter, Analysis I (in German), Springer, 3. Auflage, 1992; p. 216.

%H Wolfdieter Lang, <a href="/A096954/a096954.txt">More comments</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MachinsFormula.html">Machin's Formula</a>.

%F a(n) = denominator(M(n)), with M(n)=4*arctan(1/5, n) - arctan(1/239, n) with arctan(x, n):=sum((((-1)^k)*x^(2k+1))/(2*k+1), k=0..n).

%e A096954(7)/a(7) =

%e 170660807873601670198453967268421248219727522686104 /217292089321202035784330810406062747771759033203125

%e = 0.78539816339715...

%Y Cf. A003881, A096954.

%K nonn,frac,easy

%O 0,1

%A _Wolfdieter Lang_, Jul 23 2004

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Last modified March 29 09:14 EDT 2024. Contains 371268 sequences. (Running on oeis4.)