

A260799


Decimal expansion of the continued fraction e/(Pi+e/(Pi+e/(...))).


2



7, 0, 6, 4, 1, 3, 1, 3, 4, 0, 8, 7, 3, 0, 0, 0, 6, 9, 2, 7, 4, 1, 4, 3, 9, 4, 6, 1, 3, 9, 5, 0, 0, 2, 5, 5, 3, 3, 5, 7, 0, 6, 0, 8, 1, 2, 1, 9, 5, 2, 1, 1, 1, 4, 5, 8, 2, 4, 1, 5, 8, 6, 6, 8, 8, 3, 3, 7, 6, 1, 5, 3, 4, 4, 0, 2, 2, 7, 2, 3, 7, 0, 6, 0, 2, 5, 3, 9, 0, 1, 7, 9, 9, 2, 6, 3, 6, 6, 6, 1, 8, 4, 7, 0, 0
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OFFSET

0,1


COMMENTS

Also the positive solution of the equation x*(x+Pi)=e, and the unique attractor of the real mapping M(x)=e/(Pi+x), with e being the Euler number. The negative solution of the equation is an invariant point, but not an attractor, of M(x) and does not lead to a convergent c.f.


LINKS



FORMULA

Equals (sqrt(Pi*Pi+4*e)Pi)/2.


EXAMPLE

0.706413134087300069274143946139500255335706081219521114582415866883...
The negative solution of the equation is (a+Pi) =
3.84800578767709330773678732941900313953287548059462693555736045919...


MATHEMATICA

RealDigits[(Sqrt[Pi^2 + 4*E]  Pi)/2, 10, 120][[1]] (* Amiram Eldar, May 25 2023 *)


PROG

(PARI) (sqrt(Pi*Pi+4*exp(1))Pi)/2


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



