I have been recently reading about properties of Legendre functions in several sources and cannot seem to find any properties of Legendre functions of the second kind with negative integer degree. For example, in the Digital Library of Mathematical Functions and in Lebedev's book on special functions, they usually state a property about $Q_{\nu}^{\mu}$ only for $\nu\neq-1,-2,...$. Does anyone know why this is? For the functions of the first kind, there exists a relation $P_{\nu}=P_{-\nu-1}$. Is there a similar relationship for $Q_{\nu}$?
2026-02-23 15:06:15.1771859175
Legendre functions of the second kind with negative integer degree
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