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This "machine," described in the abstract here:

<https://phys.org/news/2019-07-ramanujan-machine-automatically-conjectures-fundamental.html>

has generated continued fractions for many fundamental constants. Two examples are given in the abstract, one for e, and another for π [actually, for 4/(π – 2)]. (Where π means pi, not the letter n.)

They might be worth exploring on your favorite HP calculator.

I haven't attempted to access the full paper, which may be behind a paywall anyway. The amusement may have exhausted itself with e and π, however.

(07-17-2019 01:24 AM)telemachos Wrote: [ -> ]I haven't attempted to access the full paper, which may be behind a paywall anyway.

It isn't.

Quote:The amusement may have exhausted itself with e and π, however.

It hasn't.

V.
.

The Ramanujan Machine: Automatically Generated Conjectures on Fundamental Constants is non-pay downloadable at arxiv.

BEST!
SlideRule

Thank-you for this. That new e one is beautiful.

(07-21-2019 10:25 AM)BruceH Wrote: [ -> ]That new e one is beautiful.

I’ve tried a variant on the wp34s:

Code:

001 LBL A

002 FILL

003 INC X

004 RCL/ Y

005 1/x

006 RCL+ Y

007 DSE Y

008 BACK 004

009 1/x

010 2

011 +

012 END

27 A 1 e^x - —> 0.

telemachos

Valentin Albillo

SlideRule

BruceH

Gerson W. Barbosa