Spherical Harmonics, Hermite and Other Special Polynomials etc.

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Discussion Overview

The discussion revolves around the study of spherical harmonics, Hermite polynomials, and other special functions, focusing on resources for learning these topics and their relevance in modern computational contexts.

Discussion Character

  • Exploratory, Debate/contested

Main Points Raised

  • One participant inquires about good books for learning spherical harmonics and related special functions.
  • Another participant recommends "Special Functions & Their Applications" by Lebedev, noting its thorough coverage and practical problems.
  • A participant expresses skepticism about the necessity of studying these functions, suggesting that computer algebra systems (CAS) can handle them more effectively than individuals.
  • This skepticism is challenged by another participant who questions whether this reasoning implies that foundational arithmetic skills should also be abandoned.
  • Another viewpoint suggests that these functions typically arise in the context of differential equations, proposing that a differential equations textbook might be a suitable resource.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of studying special functions in light of modern computational tools, indicating a lack of consensus on their educational value.

Contextual Notes

The discussion includes assumptions about the capabilities of CAS and the educational implications of relying on technology for mathematical manipulation, which remain unresolved.

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Whats a good book to learn about these topics?
 
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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!
 
looks good, thanks.
 
i don't understand the point of studying these functions anymore considering any good CAS will manipulate them much better than you ever will.
 
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?
 
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.
 

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