It must be the first place to go to know a function!]]>

That site contains many functions. Wolfram is quickly becoming the place to go.

]]>Me modest, humbug! Nah, no one has read any of it.

This may be false!!

]]>I think the Buddha is giving you good advice.

]]>Thanks for telling one more new math fact!]]>

You are a polymath, I am a wannabe

Hope nobody sees that. I think you are overestimating me.

A long time ago Riemann proved that certain series could be rearranged to sum to any value you want. It is called the Riemann Rearrangement theorem. Now Riemann had a knack for never doing anything useful so he is greatly admired by mathematicians. Anyway, some numerical analysts discovered that using his theorem that you could speed up the convergence of slowly converging alternating series by rearranging them.

The effect is quite amazing when it works. In this case I used it on the equation rather than the numbers.

This where it all starts, incidentally Maple uses this series for it's Stirling numbers of the second kind.

From that many approximations are possible. That is how he got his on that page.

]]>I don't know such advanced stuffs, so may not be able to understand how you derived it. I have heard only 'Riemann hypothesis', is it the same Riemann in 'Riemann Rearrangement'?

You are a polymath, I am a wannabe ]]>

Did you derive that, in a day?!]]>

This monstrosity will respond well for values where n ≥ 5k

It also might blow up for some particular values. It was done using the Riemann Rearrangement Algorithm.

]]>Thanks for trying that out

]]>The literature for an asymptotic approximation is scarce. Seems like they are holding on to that one. I did some work on one myself.

While trying to get my own this one pops up

It was not as bad as we thought because we are using it wrong. There are improvements to it but the amount calculation grows with each one.

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