A369880 Decimal expansion of sinh(Pi/2)/(Pi/2)^2.

9, 3, 2, 6, 8, 1, 3, 1, 4, 7, 8, 6, 3, 5, 1, 0, 1, 7, 7, 7, 3, 6, 9, 7, 5, 5, 7, 8, 0, 7, 9, 9, 0, 2, 3, 5, 0, 6, 6, 1, 9, 2, 0, 9, 3, 8, 7, 6, 9, 7, 5, 3, 1, 5, 4, 5, 6, 3, 4, 1, 2, 6, 4, 4, 0, 3, 1, 5, 6, 8, 4, 7, 9, 2, 1, 1, 6, 4, 4, 1, 1, 3, 9, 5, 6, 1, 9, 6, 2, 2, 8, 8, 5, 3, 9, 6, 5, 3, 8, 7, 4, 1, 7, 7, 1

Offset: 0

Author

Amiram Eldar, Feb 04 2024

Keywords

• nonn
• cons

Examples

			0.93268131478635101777369755780799023506619209387697...
		

References

• József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 424.

Links

• Jonathan M. Borwein and Peter B. Borwein, Strange series and high precision fraud, The American Mathematical Monthly, Vol. 99, No. 7 (1992), pp. 622-640. See p. 629, eq. (3.6); alternative link.

Crossrefs

Cf. A000120, A019669, A060294, A096111, A091476, A185199, A258232, A308716, A367959.

Programs

Mathematica

RealDigits[Sinh[Pi/2]/(Pi/2)^2, 10, 120][[1]]

PARI

sinh(Pi/2)/(Pi/2)^2

Formula

Equals A060294 * A308716 = A308716 / A019669 = A185199 * A367959 = A367959 / A091476 = A367959 / A019669^2.

Equals Sum_{k>=0} (-1/16)^A000120(k)/D(k)^4, where D(k) = A096111(k-1) for k >= 1, and D(0) = 1 (Borwein and Borwein, 1992).