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In mathematics, the polygamma function of order m is a meromorphic function on and defined as the (m+1)-thderivative of the logarithm of the gamma function: Thus holds where ψ(z) is the digamma function and Γ(z) is the gamma function.They are holomorphic on . At all the nonpositive integers these polygamma functions have a pole of order m + 1. The function ψ(1)(z) is sometimes called the trigamma function.

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• Polygamma function
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• In mathematics, the polygamma function of order m is a meromorphic function on and defined as the (m+1)-thderivative of the logarithm of the gamma function: Thus holds where ψ(z) is the digamma function and Γ(z) is the gamma function.They are holomorphic on . At all the nonpositive integers these polygamma functions have a pole of order m + 1. The function ψ(1)(z) is sometimes called the trigamma function.
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• In mathematics, the polygamma function of order m is a meromorphic function on and defined as the (m+1)-thderivative of the logarithm of the gamma function: Thus holds where ψ(z) is the digamma function and Γ(z) is the gamma function.They are holomorphic on . At all the nonpositive integers these polygamma functions have a pole of order m + 1. The function ψ(1)(z) is sometimes called the trigamma function.
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