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New way of calculating Pi

So according to a new physics paper there's a new and more effective way of calculating Pi.
(Phys. Rev. Lett. 132, 221601 (2024) - Field Theory Expansions of String Theory Amplitudes (aps.org))

This results in this formula:

So i tried to implement it, and i don't get it to work, i don't see what i've missed. Check it out?

(I've tried some variants, as if the ending n-1 should be an exponent instead, but none really works.

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Qestit Systems
Message 1 of 10
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Re: New way of calculating Pi

I don't know what lambda is or what it means, but set lambda to 4,72439077.

Message 2 of 10
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Solution
Accepted by Yamaeda

Re: New way of calculating Pi

The subscript notation corresponds to the Pochhammer function (as explained in the paper):

Regards,

Raphaël.

Message 3 of 10
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Re: New way of calculating Pi

The Numberphile YouTube channel did a video about this. They even interviewed the paper's authors who explained that the method they found was only more effective than another specific way of calculating pi and that there are much more effective ways to calculate pi.

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Re: New way of calculating Pi

Thanks, Raphael, for answering my question before I asked it!  It has been a few years (!) since I messed with Combinatorics.  Somewhere I think I have a copy of Ralston and Wilf ...

Bob Schor

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Re: New way of calculating Pi

@raphschru wrote:

The subscript notation corresponds to the Pochhammer function (as explained in the paper):

Regards,

Raphaël.

Thanks! It was that Pochhammer that got me!

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Qestit Systems
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Re: New way of calculating Pi

In other news, they only calculated pi to two places to get Voyager out of the solar system.

Bill

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Re: New way of calculating Pi

@billko wrote:

In other news, they only calculated pi to two places to get Voyager out of the solar system.

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Re: New way of calculating Pi

@billko wrote:

In other news, they only calculated pi to two places to get Voyager out of the solar system.

They probably need a couple more to get it back also. 😉 Yes, calculating to 15 decimals is very rarely useful, but it's a fun exercise. 🙂

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