Just as [tex]Li(x)[/tex] can be used to approximate how many(adsbygoogle = window.adsbygoogle || []).push({});

prime numbers there are under a given number [tex]x[/tex],

my function [tex]B(x)[/tex], which you can find here:

http://donblazys.com/on_polygonal_numbers.pdf

can be used to approximate how many

polygonal numbers of rank greater than [tex]2[/tex]

there are under a given number [tex]x[/tex].

What makes this function really interesting is that

it seems torequirea constant [tex]\alpha[/tex]

that either, or is very,isveryclose to

the actual "experimental value" of the.fine structure constant !

Thus, this function presents us with a wonderful mystery.

Is the actualfine structure constantrequired

in order to achieve the best possible approximation

(meaning the lowest possible upper bound)

for how many polygonal numbers of rank greater than [tex]2[/tex]

there are under a given number [tex]x[/tex] ?

Don.

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# Counting Function for Polygonal Numbers of Rank Greater Than 2.

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