A special function 
corresponding to a polygamma
function 
with 
,
given by
 |
(1)
|
An alternative function
 |
(2)
|
is sometimes called the trigamma function, where
 |
(3)
|
Sums and differences of 
for small integers 
and 
can be expressed in terms of 
, Catalan's constant 
, and Clausen
functions. For example,
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
|
 |  |  |
(7)
|
 |  |  |
(8)
|
 |  |  |
(9)
|
 |  |  |
(10)
|
 |  |  |
(11)
|
 |  |  |
(12)
|
 |  |  |
(13)
|
In general,
 |
(14)
|
(Lewin 1991).
)
and Trigamma (
)
Functions."