A105419 -id:A105419 - cp's OEIS frontend

A335930 Decimal expansion of the arclength on y = sin(x) from (0,0) to (Pi,0).

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

Offset: 1

Clark Kimberling, Jul 01 2020

Also the arclength between consecutive points of intersection of y = sin(x) and y = cos(x).

			arclength = 3.8201977890277120179047620821714432919099676146...

Cf. A335928, A335929, A335931, A335932.

Cf. A000796, A010466, A053004, A062539, A105419, A256667, A257407.

r = NIntegrate[Sqrt[1 + Cos[t]^2], {t, 0, Pi}, WorkingPrecision -> 200]
RealDigits[r][[1]]
First[RealDigits[Sqrt[8]*EllipticE[1/2], 10, 100]] (* Paolo Xausa, Nov 14 2024 *)

From Paolo Xausa, Nov 14 2024: (Start)
Equals Pi/A062539 + A062539 = A053004 + A062539.
Equals A010466*A257407. (End)
Equals A105419/2 = 2*A256667. - Hugo Pfoertner, Nov 14 2024

A257407 Decimal expansion of E(1/sqrt(2)) = 1.35064..., where E is the complete elliptic integral.

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Apr 22 2015

This constant is sometimes expressed as E(1/2), with a different convention of argument (Cf. Mathematica).

			1.3506438810476755025201747353387258413495223669243545453232537...

Jonathan Borwein, David H. Bailey, Mathematics by Experiment, 2nd Edition: Plausible Reasoning in the 21st Century, CRC Press (2008), p. 145.

G. C. Greubel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Elliptic Integral of the Second Kind
Wikipedia, Complete elliptic integral of the second kind

Cf. A010466, A053004, A062539, A076390, A093341, A105419.

evalf(EllipticE(1/sqrt(2)),120); # Vaclav Kotesovec, Apr 22 2015

RealDigits[EllipticE[1/2], 10, 106] // First

Equals (4*B^2 + Pi)/(4*sqrt(2)*B), where B is the lemniscate constant A076390.
Equals Pi^(3/2)/Gamma(1/4)^2 + Gamma(1/4)^2/(8*Pi^(1/2)).
Equals (agm(1,sqrt(2))+Pi/agm(1,sqrt(2)))/sqrt(8) = (A053004+A062539)/A010466. - Gleb Koloskov, Jun 29 2021

cp's OEIS Frontend

A335930 Decimal expansion of the arclength on y = sin(x) from (0,0) to (Pi,0).

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