Trigamma Function (original) (raw)
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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 integers
and
can be expressed in terms of
, Catalan's constant
, and Clausen functions. For example,
In general,
(14) |
---|
(Lewin 1991).
See also
Clausen Function, Digamma Function, Polygamma Function
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References
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.Lewin, L. (Ed.). Structural Properties of Polylogarithms. Providence, RI: Amer. Math. Soc., 1991.
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Cite this as:
Weisstein, Eric W. "Trigamma Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TrigammaFunction.html