A096954 Numerators of rational approximation to Pi/4 from Machins's formula.

951, 1339849258, 9569810428334921, 19132121777295048135244, 81963468350564671450762204559, 1287504688596138051498743351405666674, 23901655485793371607250742363386659018053931

Offset: 0

Author

Wolfdieter Lang, Jul 23 2004

Keywords

• nonn
• frac
• easy

Comments

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

Denominators are given in A096955.

Examples

			a(2)/A096955(2) = 9569810428334921/12184551018734375 = .78540...
		

References

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

Links

• Wolfdieter Lang, More comments.
• Eric Weisstein's World of Mathematics, Machin's Formula.

Crossrefs

Cf. A003881, A096955.

Formula

a(n)=numerator(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).