Spherical Harmonics, Hermite and Other Special Polynomials etc.

In summary, When looking for a book to learn about the topics of special functions and their applications, Lebedev's Special functions & Their Applications (Dover books) is a good option. It thoroughly covers these topics and includes worked out problems in the "Applications" chapter. It is also inexpensive. However, one person questions the relevance of studying these functions since computer algebra systems can manipulate them more efficiently. Another suggests that a book on differential equations might be a better resource for these topics.
  • #1
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Whats a good book to learn about these topics?
 
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  • #2
Lebedev, Special functions & Their Applications (Dover books) covers these thoroughly, includes many worked out problems in the "Applications" chapter accompanying each topic, and is inexpensive!
 
  • #3
looks good, thanks.
 
  • #4
i don't understand the point of studying these functions anymore considering any good CAS will manipulate them much better than you ever will.
 
  • #5
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.

So I guess we should stop teaching children how to add, multiply, and do algebra?
 
  • #6
Don't these usually crop up from the study of differential equations? So a differential equations book might be the correct place? Any decent DE book should cover this stuff I think.
 

FAQ: Spherical Harmonics, Hermite and Other Special Polynomials etc.

What are spherical harmonics?

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.

What are Hermite polynomials?

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.

How are spherical harmonics and Hermite polynomials related?

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.

Can spherical harmonics and Hermite polynomials be used in other fields besides physics and mathematics?

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.

What are other special polynomials besides spherical harmonics and Hermite polynomials?

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.

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