Appendix C

 

Zeta-exponential function

 

As we know the exponential function is:


The Riemann Zeta function is:



Combine the exponential function and zeta function, and then we can have a new function, which we temporally called the zeta-exponential function as follows:

 

 

Then we will get:

 

 

Thus:

 

 

Thus:

 

 

Thus:

 

 

Thus, we have:

 


The above equation is the
Fourier serial of the complex zeta-exponential function.

 

 

 

As we know:

 

 

Thus:

 

 

 

As we know for the exponential function, we have:

 

 

 

 

Similar to the exponential function, the complex zeta-exponential function has the following relationship:

 

 

 

 

 

for m =1 and , thus we have

 

 

for m =1 and , thus we have

 

 

 


What is the electron spin?
ISBN 0-9743974-9-0
Copyright 2003
Gengyun Li
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