Polygamma Function - Reflection Relation

Reflection Relation

(-1)^m \psi^{(m)} (1-z) - \psi^{(m)} (z) = \pi \frac{d^m}{d z^m} \cot{(\pi z)} = \pi^{m+1} \frac{P_m(\cos(\pi z))}{\sin^{m+1}(\pi z)}

where is alternatingly an odd resp. even polynomial of degree with integer coefficients and leading coefficient . They obey the recursion equation with .

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