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Whats a good book to learn about these topics?
ice109 said:i don't understand the point of studying these functions anymore considering any good CAS will manipulate them much better than you ever will.
Spherical harmonics are a set of mathematical functions used to represent solutions to Laplace's equation in spherical coordinates. They are commonly used in physics and engineering to describe the behavior of waves and other phenomena in spherical systems.
Hermite polynomials are a set of orthogonal polynomials that are solutions to the Hermite differential equation. They are commonly used in probability theory and quantum mechanics to represent wavefunctions and probability distributions.
Spherical harmonics and Hermite polynomials are both special types of orthogonal polynomials. In fact, the spherical harmonics can be expressed as a linear combination of Hermite polynomials, making them closely related.
Yes, spherical harmonics and Hermite polynomials have applications in various fields such as computer graphics, signal processing, and image analysis. They are useful for representing and analyzing data that is defined on a spherical surface or in higher dimensions.
There are many other families of special polynomials, such as Legendre polynomials, Chebyshev polynomials, and Laguerre polynomials. Each of these have their own unique properties and applications in different fields of mathematics and science.