Trigamma function
Mathematical function / From Wikipedia, the free encyclopedia
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For Barnes's gamma function of 3 variables, see triple gamma function.
In mathematics, the trigamma function, denoted ψ1(z) or ψ(1)(z), is the second of the polygamma functions, and is defined by
- .
It follows from this definition that
where ψ(z) is the digamma function. It may also be defined as the sum of the series
making it a special case of the Hurwitz zeta function
Note that the last two formulas are valid when 1 − z is not a natural number.