The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A064853

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A064853

Lemniscate constant.
(history; published version)

#39 by Michael De Vlieger at Sat Sep 24 08:17:51 EDT 2022

STATUS

reviewed

approved

#38 by Michel Marcus at Sat Sep 24 01:50:03 EDT 2022

STATUS

proposed

reviewed

#37 by Stefano Spezia at Fri Sep 23 19:09:48 EDT 2022

STATUS

editing

proposed

Discussion

Fri Sep 23

19:46

Jon E. Schoenfield: You're welcome!  :-)

#36 by Stefano Spezia at Fri Sep 23 19:09:27 EDT 2022

FORMULA

Equals 4*Integral_{x=0..Pi/2} 1/sqrt(2*(1 - (1/2)*sin(x)^2)) dx [Gauss, 1799] (see Faulhuber et al.).

STATUS

proposed

editing

Discussion

Fri Sep 23

19:09

Stefano Spezia: Yes. Added. Thanks much Jon

#35 by Stefano Spezia at Fri Sep 23 17:20:17 EDT 2022

STATUS

editing

proposed

Discussion

Fri Sep 23

18:05

Jon E. Schoenfield: Should there be a “dx” in the integral?

#34 by Stefano Spezia at Fri Sep 23 14:52:49 EDT 2022

FORMULA

Equals 2*A002193sqrt(2)*A093341. (End)

#33 by Stefano Spezia at Fri Sep 23 14:51:15 EDT 2022

FORMULA

Equals 2*sqrt(2)A002193*A093341. (End)

CROSSREFS

Cf. A002193, A019727, A062539, A068466, A085565, A093341.

#32 by Stefano Spezia at Fri Sep 23 14:47:41 EDT 2022

FORMULA

From Stefano Spezia, Sep 23 2022: (Start)

Equals 4*Integral_{x=0..Pi/2} 1/sqrt(2*(1 - (1/2)*sin(x)^2)) [Gauss, 1799] (see Faulhuber et al.). - _Stefano Spezia_, Sep 23 2022

Equals 2*sqrt(2)*A093341. (End)

#31 by Stefano Spezia at Fri Sep 23 14:44:53 EDT 2022

LINKS

Markus Faulhuber, Anupam Gumber, and Irina Shafkulovska, <a href="https://arxiv.org/abs/2209.04202">The AGM of Gauss, Ramanujan's corresponding theory, and spectral bounds of self-adjoint operators</a>, arXiv:2209.04202 [math.CA], 2022, p. 15.

FORMULA

Equals 4*Integral_{x=0..Pi/2} 1/sqrt(2*(1 - (1/2)*sin(x)^2)) [Gauss, 1799] (see Faulhuber et al.). - Stefano Spezia, Sep 23 2022

#30 by Stefano Spezia at Fri Sep 23 14:37:13 EDT 2022

FORMULA

Equals 4*Integral_{x=0..Pi/2} 1/sqrt(2*(1 - (1/2)*sin(x)^2)) [Gauss, 1799]. - Stefano Spezia, Sep 23 2022

STATUS

approved

editing