# Questions tagged [legendre-polynomials]

For questions about Legendre polynomials, which are solutions to a particular differential equation that frequently arises in physics.

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### Is the Gram-Schmidt Orthogonalization process for functions the same as it is for vectors? [closed]

I was not able to find resources online and was wondering so since it would greatly help me with my work if I can directly apply what I have learned from linear algebra.
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### Multidimensional Legendre polynomials?

Legendre polynomials can be given by several expressions, but perhaps the most compact way to represent them is by Rodrigues' formula as $$P_n(x) = \frac{1}{2^n n!} \frac{d^n}{dx^n} (x^2 - 1)^n.$$ I ...
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### Interpolation and general Gaussian quadrature

I just finished a course on numerical mathematics, and have become quite interested in interpolation and how it ties into numerical integration. What suprised me while studiyng quadrature was the fact ...
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### "Legendre-type" integrals involving $\frac{dt}{\sqrt{t^2-2t\cos(\theta)+1}}$

Summing Legendre polynomials $P_{l}(\cos\theta)$ often leads to expressions containing $\frac{1}{\sqrt{t^2-2t\cos\theta+1}}$, as this is the generating function for the Legendre polynomials. I want to ...
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