The Elsasser function is defined by the integral
![E(y,u)=int_(-1/2)^(1/2)exp[-(2piyusinh(2piy))/(cosh(2piy)-cos(2pix))]dx.](/images/equations/ElsasserFunction/NumberedEquation1.svg) |
(1)
|
This integral is a normalized form of the transmission function for the regular Elsasser band model (Liou 1980, pp. 100-101). For 
and 
, it can also be written
as
 |
(2)
|
where 
is the modified Bessel function
of the first kind (Liou 1980, p. 101).
Special values, using the continuous extension at 
, include
 |  |  |
(3)
|
 |  |  |
(4)
|
