Dear Bill and math-funsters, Just in case some of you haven't seen the call, here it is. We'd be happy to debate the use of Riemann surfaces for Lambert W or Dilbert Lambda at the meeting! Cheers, Rob. Celebrating 20 years of the Lambert W Function ===================================== 25-28 July 2016 Western University (University of Western Ontario) London, Ontario, Canada Web site: www.apmaths.uwo.ca/~djeffrey/LambertW/LambertW.html Call for speakers (papers) In 1996, the first comprehensive survey of the Lambert W function was published. To celebrate 20 years since that publication, Western University will host a workshop on the Lambert W function and on related special and elementary functions. Talks on applications, including physics, biology, sociology and computational science are welcome. Mathematical applications to areas such as combinatorics, delay-differential equations and so on are also welcome. Generalizations and other nonlinear eigenvalue functions and matrix functions are especially welcome. Graduate students are particularly encouraged to contribute and attend. Please see the website for further details, or mail rcorless@uwo.ca =========== Sent on behalf of Rob Corless Western University, Applied Mathematics Middlesex College, Rm 255 1151 Richmond St. N., London, ON N6A 5B7 On 3 June 2016 at 23:26, Bill Gosper <billgosper@gmail.com> wrote:
Graphically, how it would look entails the usual hard problem of plotting a complex valued function of a complex argument. But by "how it would look", I meant how you could invoke it and interpret it based on a Riemann surface description vs a branch number. I'm not sure I've ever seen this, even for an elementary function. If you have a workable idea, Wolfram might even *give* you a Mathematica. Meanwhile, if you need something plotted, email it to me. --rwg
On 2016-06-03 16:51, Dan Asimov wrote:
I would love to tell y'all how it would look in Mathematica if only I had Mathematica.
—Dan P.S. I have remote access to a text-based Mathematica, but not to graphics.
On Jun 3, 2016, at 4:20 PM, Bill Gosper <billgosper@gmail.com> wrote:
On 2016-06-03 07:03, Veit Elser wrote:
Two fun W (Lambert function) facts:
1) The Taylor series of W records the number of spanning trees of the complete graphs.
2) If 1/2+i y_n is the nth zero of the Riemann zeta function on the critical line, then asymptotically (large n)
y_n ~ 2 pi (n-11/8)/ W((n-11/8)/e)
-Veit
Less amazing, but useful: They appear in an inelegant but efficient series solution to Kepler's equation: http://www.tweedledum.com/rwg/pizza.html It's a bit disappointing that W doesn't solve Kepler's more elegantly. But suppose we posit that E(ε,M) := Kepler(ε,M) solves M = E - ε sin E . Does this dyadic function Kepler subsume Lambert W as a special case? If so, maybe we should embrace it. Failing that, I think "Dilbert Lambda"(y), which solves y = Λ exp Λ², is usually nicer than W.
On Jun 2, 2016, at 10:28 PM, Dan Asimov <dasimov@earthlink.net>
wrote:
Thanks. I vastly prefer the Lambert W function when it is not defined
with a branch cut but is allowed to extend to it full Lambertness on a Riemann surface.
Whether considering the Lambert function or the more simply defined
function of which it is the inverse function:
f(z) = z exp(z),
the aforesaid Riemann surface is just the subset of C^2 defined as
{(z,w) | z = w exp(w)}.
This is, in my opinion, the appropriate object of study.
—Dan
All we need is for you to tell us how it would look in Mathematica. --rwg
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