High Quality Content by WIKIPEDIA articles! In mathematics, the trigamma function, denoted ?1(z), is the second of the polygamma functions, and is defined by psi_1(z) = frac{d^2}{dz^2} lnGamma(z). It follows from this definition that psi_1(z) = frac{d}{dz} psi(z) where ?(z) 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 ?1(z) = ?(2,z). Note that the last two formulae are valid when 1-z is not a natural number.

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