The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A261745 Decimal expansion of -sm(-1), where sm(t) is the Dixonian elliptic function sm(t). 0
 1, 2, 0, 5, 4, 1, 5, 1, 5, 1, 4, 0, 2, 9, 8, 3, 1, 5, 4, 8, 3, 1, 4, 1, 1, 3, 7, 5, 7, 8, 4, 4, 8, 8, 0, 1, 2, 0, 7, 2, 7, 0, 4, 1, 9, 1, 8, 8, 2, 2, 4, 9, 5, 8, 1, 0, 9, 3, 2, 7, 1, 8, 2, 3, 5, 4, 4, 7, 6, 4, 8, 8, 1, 0, 6, 5, 5, 1, 1, 2, 5, 5, 6, 3, 2, 1, 7, 0, 3, 6, 5, 2, 2, 9, 3, 7, 9, 8, 9, 0, 8, 0, 6, 7, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In the context of particle physics and in the case of a Yule branching process with two types of particles, this constant appears in the asymptotic expression of the probability that all particles be of the second type at time t as exp(-t)*smh(1). LINKS Table of n, a(n) for n=1..105. Eric van Fossen Conrad and Philippe Flajolet, The Fermat cubic, elliptic functions, continued fractions and a combinatorial excursion, Séminaire Lotharingien de Combinatoire 54 (2006), Article B54g, page 20. Eric Weisstein's MathWorld, Weierstrass Elliptic Function EXAMPLE 1.205415151402983154831411375784488012072704191882249581... MATHEMATICA sm[z_] := 6*WeierstrassP[z, {0, 1/27}]/(1 - 3*WeierstrassPPrime[z, {0, 1/27}]); N[-sm[-1], 105] // RealDigits // First (* or, without using the Weierstrass P function: *) nint[y_?NumericQ] := NIntegrate[1/(1 + w^3)^(2/3), {w, 0, y}, WorkingPrecision -> 105]; smh[t_] := y /. FindRoot[nint[y] == t, {y, t}, WorkingPrecision -> 105]; N[smh[1], 105] // RealDigits // First CROSSREFS Cf. A104133, A104134. Sequence in context: A086280 A349950 A164976 * A083714 A215481 A262933 Adjacent sequences: A261742 A261743 A261744 * A261746 A261747 A261748 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Aug 30 2015 STATUS approved

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

Last modified August 11 19:17 EDT 2024. Contains 375073 sequences. (Running on oeis4.)