sennheiser vs akg. ( HD650 or DT 990 or AKG Q701 or AKG 702 or AKG and any other AKG or headphones)
Mar 20, 2013 at 10:55 PM Post #19 of 24
Brilliant!
 
Mar 21, 2013 at 9:39 PM Post #21 of 24
Quote:
 
Not quite:
 
17/10 = 1.7
 
So the E17 is only 1.7 times better.

 
No, that's not how Fiio product numbering works.  Fiio uses the Riemann zeta function to relate product performance and number.
 
On the real line with 
size]
, the Riemann zeta function can be defined by the integral
 

 
where 
size]
 is the gamma function. If 
size]
 is an integer 
size]
, then we have the identity
 
 
=


 
So,
 

 
 
To evaluate 
size]
, let 
size]
 so that 
size]
 and plug in the above identity to obtain
 
 =
 


 
Integrating the final expression in gives 
size]
, which cancels the factor 
size]
 and gives the most common form of the Riemann zeta function,
 

 
 
which is sometimes known as the p-series.
 
 
 
The Riemann zeta function can also be defined in terms of multiple integrals by,
 

and as a Mellin transform by,
 

 
or 
size]
, where 
size]
 is the fractional part.
 
 
 
The Riemann zeta function can also be defined in the complex plane by the contour integral
 

 
for all 
size]
, where the contour is illustrated above.
 
 
 
The Riemann zeta function is related to the Dirichlet lambda function 
size]
 and Dirichlet eta function 
size]
 by
 

 
and
 

 
 
 
 
It is also related to the Liouville function 
size]
 by
 

 
Furthermore,
 

 
where 
size]
 is the number of distinct prime factors of 
size]
.
 
 
Perry
 
Dec 21, 2013 at 10:29 AM Post #24 of 24
No, that's not how Fiio product numbering works.  Fiio uses the Riemann zeta function to relate product performance and number.

On the real line 
with 
size]

, the Riemann zeta function can be defined by the integral





where 
size]

 is the gamma function
. If 
size]

 is an 
i
nteger 
size]

, then we have the identity




=






So,





To evaluate 
size]

, let 
size]

 so that 
size]

 and plug in the above identity to obtain



 =
 






Integrating the final expression in
 gives 
size]

, which cancels the factor 
size]

 and gives the most common form of the Riemann zeta function,






which is sometimes known as the p-series.



The Riemann zeta function can also be defined in terms of multiple integrals by,




and as a Mellin transform by,




or 
size]

, where 
size]

 is the fractional part.




The Riemann zeta function can also be defined in the complex plane by the contour integral





for all 
size]

, where the co
ntour is illustrated above.




The Riemann zeta function is related to the Dirichlet 
lambda
 
function 
size]

 and Dirichlet eta function
 
size]

 by





and







It is also related to the Liouville function
 
size]

 by





Furthermore,




where 
size]

 is the number of distinct prime factors
 of 
size]

.


Perry
:horse:+1
 

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