Trigamma Function
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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
integral 
and 
can be expressed
in terms of Catalan's constant 
and 
. For example,
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
|
 |  |  |
(7)
|
 |  |  |
(8)
|
 |  |  |
(9)
|
 |  |  |
(10)
|
 |  |  |
(11)
|
 |  |  |
(12)
|
 |  |  |
(13)
|
SEE ALSO: Digamma Function, Polygamma
Function
REFERENCES:
Referenced on Wolfram|Alpha: Trigamma Function
CITE THIS AS:
Jeffreys, H. and Jeffreys, B. S. "The Digamma (
) and Trigamma
(
) Functions." Methods
of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University
Press, pp. 465-466, 1988.
Weisstein, Eric W. "Trigamma Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/TrigammaFunction.html
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asymptotes (2x^3 + 4x^2 - 9)/(3 - x^2)