A367961 -id:A367961 - cp's OEIS frontend

A367960 Decimal expansion of tanh(Pi/2).

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

Offset: 0

R. J. Mathar, Dec 06 2023

			0.91715233566727434637309...

Calvin C. Clawson, Mathematical Mysteries: The Beauty and Magic of Numbers, Springer, 2013. See p. 225.

Cf. A367961, A367959, A308715, A083124 (cont. frac).

Maple
```
evalf(tanh(Pi/2)) ;
```

First[RealDigits[Tanh[Pi/2],10,100]] (* Paolo Xausa, Dec 06 2023 *)

Equals 1/A367961 = A367959 / A308715 = (2/Pi)*A228048.

Equals (e^Pi - 1)/(e^Pi + 1) = K_{n>0} Pi^(2-[n=1])/(4*n - 2) (see Clawson at p. 225). - Stefano Spezia, Jul 01 2024

A367976 Decimal expansion of Sum_{k >= 0} (-1)^k/(1+k^2).

Original entry on oeis.org

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

Offset: 0

R. J. Mathar, Dec 07 2023

			0.636014527491066581475118291836...

Cf. A113319.

1/4*(2-Pi*tanh(Pi/2)+Pi*coth(Pi/2)) ; evalf(%) ;

RealDigits[(1 + Pi*Csch[Pi])/2, 10, 120][[1]] (* Amiram Eldar, Dec 11 2023 *)

sumalt(k=0, (-1)^k/(1+k^2)) \\ Michel Marcus, Dec 07 2023

Equals (2-Pi*tanh(Pi/2)+Pi*coth(Pi/2))/4 = (1 - A228048 + Pi/2*A367961)/2.
From Amiram Eldar, Dec 11 2023: (Start)
Equals (1 + Pi/sinh(Pi))/2.
Equals Integral_{x>=0} (cos(x)/cosh(x))^2 dx. (End)
Equals (1+A090986)/2. - R. J. Mathar, Dec 13 2023

cp's OEIS Frontend

A367960 Decimal expansion of tanh(Pi/2).

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