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A222494 Decimal expansion of the length of the dipole curve. 1
3, 5, 8, 2, 7, 8, 6, 8, 3, 1, 8, 5, 2, 2, 0, 4, 1, 7, 5, 1, 5, 4, 7, 0, 7, 8, 5, 9, 1, 5, 5, 6, 1, 0, 6, 6, 6, 3, 9, 2, 0, 8, 5, 0, 2, 3, 4, 7, 5, 5, 4, 8, 0, 7, 7, 4, 8, 0, 4, 6, 2, 7, 8, 4, 7, 6, 8, 8, 9, 7, 3, 2, 7, 9, 5, 2, 6, 5, 2, 5, 5, 4, 7, 0, 4, 2, 4, 8, 5, 1, 6, 1, 3, 1, 7, 5, 5, 2, 4, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The Cartesian equation of the dipole curve, also known as the Playfair curve, is (x^2 + y^2)^3 = a^4*x^2, where the parameter 'a' is the area and the width of one lobe. The computation of the length of one lobe is done here with a=1.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

Robert Ferréol, Courbe du dipole (in French)

Jan Wassenaar, Dipole curve

FORMULA

Equals 2*Integral_{x=0..1} sqrt(1 + f'(x)^2), where f(x) = sqrt(x^(2/3) - x^2).

Equals Integral_{t=0..Pi/2} sqrt(3*cos(t)+1/cos(t)). - Jan Mangaldan, Nov 23 2020

EXAMPLE

3.582786831852204175154707859155610666392085023475548077480462784768897327952...

MATHEMATICA

2*a*Sqrt[Pi]*Gamma[5/4]*Hypergeometric2F1[-1/2, 1/4, 3/4, -3]/Gamma[3/4] /. a -> 1 // RealDigits[#, 10, 100] & // First

RealDigits[Sqrt[2 Pi] Gamma[5/4] Hypergeometric2F1[1/4, 5/4, 3/4, 3/4]/Gamma[3/4], 10, 100][[1]] (* Jan Mangaldan, Nov 22 2020 *)

PROG

(PARI) localprec(100); intnum(t=0, Pi/2, sqrt(3*cos(t)+1/cos(t))) \\ Michel Marcus, Dec 05 2020

CROSSREFS

Sequence in context: A089103 A189964 A181910 * A336238 A181918 A010617

Adjacent sequences:  A222491 A222492 A222493 * A222495 A222496 A222497

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, May 29 2013

STATUS

approved

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Last modified May 21 03:13 EDT 2022. Contains 353886 sequences. (Running on oeis4.)