Jump to content

p-adic numbers and the Ramanujan summation


Linkey

Recommended Posts

I have watched a video about the p-adic numbers:

 

 

Then, there is the Ramanujan's summation which is used in quantum mechanics (Casimir effect):

 

1+2+3+4+5+6...=-1/12

https://en.wikiversity.org/wiki/Quantum_mechanics/Casimir_effect_in_one_dimension

This forum does not support Latex maths?

Then, we have one more such summation:

1+x+x*x+x*x*x+x*x*x*x+x*x*x*x*x...=-1/(1-x)

This is simple for x<1 and for x>1 we get:

 

1+2+4+8+16+32+64...=-1

1+10+100+1000+10000...=-1/9

1+20+400+8000+160000...=-1/19

 

Can we obtain all these sums with the p-adic numbers?

Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.