Lesson plan
Trigamma function
method. In mathematics, the trigamma function, denoted or , is the second of the polygamma functions, and is defined by : \psi_1(z) = \frac{d^2}{dz^2} \ln\Gamma(z) . It follows from this definition that : \psi_1(z) = \frac{d}{dz} \psi(z) where is the digamma function. It may also be defined as the sum of the series : \psi_1(z) = \sum_{n = 0}^{\infty}\frac{1}{(z + n)^2}, making it a special case of the Hurwitz zeta function : \psi_1(z) = \zeta(2,z). Note that the last two formulas are valid when is not a natural number.
Article summary
method. In mathematics, the trigamma function, denoted or , is the second of the polygamma functions, and is defined by : \psi_1(z) = \frac{d^2}{dz^2} \ln\Gamma(z) . It follows from this definition that : \psi_1(z) = \frac{d}{dz} \psi(z) where is the digamma function. It may also be defined as the sum of the series : \psi_1(z) = \sum_{n = 0}^{\infty}\frac{1}{(z + n)^2}, making it a special case of the Hurwitz zeta function : \psi_1(z) = \zeta(2,z). Note that the last two formulas are valid when is not a natural number.
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