Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 ...Full description
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 formulæ are valid when 1-z is not a natural number.