I will denote by $P^m_l(x)$ the Legendre first kind function of order $m$ and of degree $l$, $m$ is a positive integer and $l$ is real number. I fix the value of $x\in[0,1]$ and $l=-0.5$. Is there any way the study the monotonicity of $m\to P^m_l(x)/P^m_l(-x)$.
2026-02-23 13:29:28.1771853368
Monotonicity of Legendre functions (of first kind) with respect to theirs order
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