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A249414 Decimal expansion of r_0, a universal radius associated with mapping properties of analytic functions on the unit disk and with Dirichlet's integral. 1
0, 3, 9, 4, 9, 2, 9, 2, 2, 7, 7, 1, 6, 6, 3, 5, 8, 9, 5, 1, 6, 4, 0, 3, 7, 4, 6, 9, 9, 0, 8, 1, 4, 6, 1, 1, 2, 0, 1, 0, 6, 6, 0, 4, 5, 8, 2, 4, 3, 0, 7, 0, 6, 6, 6, 9, 5, 0, 2, 7, 8, 7, 4, 2, 6, 6, 4, 5, 3, 8, 1, 5, 4, 5, 7, 7, 0, 9, 1, 7, 3, 4, 5, 7, 9, 7, 3, 4, 7, 5, 4, 8, 6, 5, 9, 1, 0, 7, 1, 2, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..100.

Steven R. Finch, Dirichlet Integral, May 15, 2008. [Cached copy, with permission of the author]

FORMULA

r_0 = (2^(1/4)*K(-sqrt(2)) - K(-1/sqrt(2)))/(2^(1/4)*K(-sqrt(2)) + K(-1/sqrt(2))), where K is the complete elliptic integral of the first kind.

EXAMPLE

0.039492922771663589516403746990814611201066045824307066695...

MAPLE

evalf((EllipticK(sqrt(2-sqrt(2))) - EllipticK(sqrt(sqrt(2)-1))) / (EllipticK(sqrt(2-sqrt(2))) + EllipticK(sqrt(sqrt(2)-1))), 120); # Vaclav Kotesovec, Oct 28 2014

MATHEMATICA

r0 = (2^(1/4)*EllipticK[-Sqrt[2]] - EllipticK[-1/Sqrt[2]])/(2^(1/4)*EllipticK[-Sqrt[2]] + EllipticK[-1/Sqrt[2]]); Join[{0}, RealDigits[r0, 10, 100] // First]

Prepend[RealDigits[2/(1 + EllipticK[Sqrt[2] - 1]/EllipticK[2 - Sqrt[2]]) - 1, 10, 100][[1]], 0] (* Jan Mangaldan, Jan 04 2017 *)

CROSSREFS

Sequence in context: A021721 A212002 A199452 * A011428 A070356 A143237

Adjacent sequences: A249411 A249412 A249413 * A249415 A249416 A249417

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Oct 28 2014

STATUS

approved

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Last modified February 7 19:35 EST 2023. Contains 360128 sequences. (Running on oeis4.)