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

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A093341 Decimal expansion of "lemniscate case". 6
1, 8, 5, 4, 0, 7, 4, 6, 7, 7, 3, 0, 1, 3, 7, 1, 9, 1, 8, 4, 3, 3, 8, 5, 0, 3, 4, 7, 1, 9, 5, 2, 6, 0, 0, 4, 6, 2, 1, 7, 5, 9, 8, 8, 2, 3, 5, 2, 1, 7, 6, 6, 9, 0, 5, 5, 8, 5, 9, 2, 8, 0, 4, 5, 0, 5, 6, 0, 2, 1, 7, 7, 6, 8, 3, 8, 1, 1, 9, 9, 7, 8, 3, 5, 7, 2, 7, 1, 8, 6, 1, 6, 5, 0, 3, 7, 1, 8, 9, 7, 2, 7, 7, 7, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, 9th printing. New York: Dover, 1972, Section 18.14.7, p. 658.

Jonathan Borwein & Peter Borwein, A Dictionary of Real Numbers. Pacific Grove, California: Wadsworth & Brooks/Cole Advanced Books & Software (1990) p. iii

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.1 Gauss' Lemniscate Constant, p. 421.

LINKS

Harry J. Smith, Table of n, a(n) for n=1,...,5000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Section 18.14.7, p. 658.

G. Mingari Scarpello, D. Ritelli, On computing some special values of hypergeometric functions, arXiv:1212.0251, eq. (4.1)

Eric Weisstein's World of Mathematics, Lemniscate Case.

FORMULA

GAMMA(1/4)^2/(4*(Pi)^(1/2)) - Pab Ter (pabrlos(AT)yahoo.com), May 24 2004

Also equals ellipticK(1/2) = Pi/2*hypergeom([1/2,1/2],[1],1/2),

or also the smallest positive root of cs(x/sqrt(2)|-1), where cs is the Jacobi elliptic function,

or also the real half-period of the Weierstrass Pe function (Cf. Finch p. 422). - Jean-François Alcover, Apr 30 2013, updated Aug 01 2014.

EXAMPLE

1.854074677301371918433850347195260046217598823521766905585928045056021... [Harry J. Smith, Jun 19 2009]

MAPLE

evalf( EllipticK(1/sqrt(2)) ); # R. J. Mathar, Aug 28 2013

MATHEMATICA

RealDigits[ N[ Gamma[1/4]^2 / (4*Sqrt[Pi]), 105]][[1]] (* Jean-François Alcover, Oct 04 2011 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 5080); x=gamma(1/4)^2/(4*(Pi)^(1/2)); for (n=1, 5000, d=floor(x); x=(x-d)*10; write("b093341.txt", n, " ", d)); } \\ Harry J. Smith, Jun 19 2009

CROSSREFS

Cf. A064853, A062539.

Sequence in context: A154509 A081885 A019609 * A134973 A030437 A200290

Adjacent sequences:  A093338 A093339 A093340 * A093342 A093343 A093344

KEYWORD

cons,nonn

AUTHOR

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Apr 26 2004

EXTENSIONS

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 24 2004

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 23 11:48 EST 2014. Contains 249842 sequences.