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rihani
rihani
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Is there any formula for computing the following integral $$\int_a^1(P^m_l)^2(x)\,dx \, ,$$$$\int_a^1(P^m_l)^2(x)\,dx \, ,\text{with} -1<a<1$$ where $P^m_l$ is the associated Legendre's function (of the first kind) of order $m\in\mathbb{N}$ and of degree $l=-0.5+it$ with $t\in\mathbb{R}$.

Is there any formula for computing the following integral $$\int_a^1(P^m_l)^2(x)\,dx \, ,$$ where $P^m_l$ is the associated Legendre's function (of the first kind) of order $m\in\mathbb{N}$ and of degree $l=-0.5+it$ with $t\in\mathbb{R}$.

Is there any formula for computing the following integral $$\int_a^1(P^m_l)^2(x)\,dx \, ,\text{with} -1<a<1$$ where $P^m_l$ is the associated Legendre's function (of the first kind) of order $m\in\mathbb{N}$ and of degree $l=-0.5+it$ with $t\in\mathbb{R}$.

redundant $a$ and redundant space
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Amir Sagiv
Amir Sagiv
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Is there any formula for computing the following integral $$\int_a^1(P^m_l)^2(x)\,dx;-1<a<1$$$$\int_a^1(P^m_l)^2(x)\,dx \, ,$$ where $P^m_l$ is the associated Legendre's function ( ofof the first kind) of order $m\in\mathbb{N}$ and of degree $l=-0.5+it$ with $t\in\mathbb{R}$.

Is there any formula for computing the following integral $$\int_a^1(P^m_l)^2(x)\,dx;-1<a<1$$ where $P^m_l$ is the associated Legendre's function ( of first kind) of order $m\in\mathbb{N}$ and of degree $l=-0.5+it$ with $t\in\mathbb{R}$.

Is there any formula for computing the following integral $$\int_a^1(P^m_l)^2(x)\,dx \, ,$$ where $P^m_l$ is the associated Legendre's function (of the first kind) of order $m\in\mathbb{N}$ and of degree $l=-0.5+it$ with $t\in\mathbb{R}$.

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rihani
rihani
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  • 2

Integral of Legendre's function

Is there any formula for computing the following integral $$\int_a^1(P^m_l)^2(x)\,dx;-1<a<1$$ where $P^m_l$ is the associated Legendre's function ( of first kind) of order $m\in\mathbb{N}$ and of degree $l=-0.5+it$ with $t\in\mathbb{R}$.