login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A105419 Decimal expansion of the arc length of the sine or cosine curve for one full period. 1
7, 6, 4, 0, 3, 9, 5, 5, 7, 8, 0, 5, 5, 4, 2, 4, 0, 3, 5, 8, 0, 9, 5, 2, 4, 1, 6, 4, 3, 4, 2, 8, 8, 6, 5, 8, 3, 8, 1, 9, 9, 3, 5, 2, 2, 9, 2, 9, 4, 5, 4, 9, 4, 4, 2, 1, 6, 0, 9, 9, 3, 3, 1, 3, 4, 9, 4, 3, 9, 1, 6, 0, 2, 4, 2, 8, 6, 5, 9, 8, 4, 2, 1, 3, 2, 3, 6, 2, 1, 7, 8, 9, 0, 2, 4, 4, 4, 9, 6, 5, 6, 4, 4, 0, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Howard Anton, Irl C. Bivens, Stephen L. Davis, Calculus, Early Transcendentals, 7th Edition, John Wiley & Sons, Inc., NY, Section 7.4 Length of a Plane Curve, page 489.

LINKS

Table of n, a(n) for n=1..105.

FORMULA

Integral_{0, 2Pi} Sqrt(1+Cos(x)^2) dx.

Also equals 4*B+Pi/B where B is the lemniscate constant A076390, or sqrt(2/Pi)*(2*gamma(3/4)^4 + Pi^2)/gamma(3/4)^2. [Jean-François Alcover, Apr 17 2013]

EXAMPLE

I=7.640395578055424035809524164342886583819935229294549442160993313...

MAPLE

evalf(4*sqrt(2)*EllipticE(1/sqrt(2)), 120); # Vaclav Kotesovec, Apr 22 2015

MATHEMATICA

RealDigits[ NIntegrate[ Sqrt[1 + Cos[x]^2, {x, 0, 2Pi}, MaxRecursion -> 12, WorkingPrecision -> 128], 10, 111][[1]]

RealDigits[ N[ 4*Sqrt[2]*EllipticE[1/2], 105]][[1]] (* Jean-François Alcover, Nov 08 2012 *)

CROSSREFS

Sequence in context: A187799 A132714 A230327 * A175996 A248940 A134982

Adjacent sequences:  A105416 A105417 A105418 * A105420 A105421 A105422

KEYWORD

cons,nonn

AUTHOR

Robert G. Wilson v, Apr 06 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 7 03:45 EST 2016. Contains 278841 sequences.