Thursday, June 20, 2019

New Num

I think I've reached a new planet. There I was musing
about what integrating fractional expressions does.
One ends up a situation where the integral can no
longer be used for reading the value of the original
function. At its simplest:




Out of curiosity, wanted to see where my two curves meet.
Only Wolfram would tell me, and I've stumbled upon a brand
new trancendental number, W, a Lambert number.

They meet at 1.763...

Rather close to the square root of pi, in fact!

So this is a unique value, where e^this value is equal to 1/this value:


How is this value arrived at? 



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