What Are the Applications of Associated Legendre Functions?

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SUMMARY

Associated Legendre functions are critical in solving partial differential equations (PDEs) on the Riemann sphere, particularly in applications related to the evolution of electric and magnetic fields. They are utilized in various fields of physics and mathematics, especially in problems involving spherical harmonics. The integration of Associated Legendre functions with other functions over the real line is essential for obtaining solutions to specific physical models.

PREREQUISITES
  • Understanding of partial differential equations (PDEs)
  • Familiarity with spherical harmonics
  • Knowledge of complex analysis, particularly the Riemann sphere
  • Basic concepts of electromagnetism related to electric and magnetic fields
NEXT STEPS
  • Research the applications of spherical harmonics in physics
  • Study the properties and applications of Associated Legendre functions
  • Explore the integration techniques involving special functions
  • Learn about the role of PDEs in modeling physical phenomena
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Mathematicians, physicists, and engineers interested in advanced applications of special functions, particularly in the context of electromagnetic theory and complex analysis.

BCox
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Hello:

What are Associated Legendre functions? What are they good for in terms of applications?
 
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I think it's used in solving partial differentials in a Riemann (complex) sphere, though not all pde's relating to physics can be visualized in a Riemann sphere... few actually.

But some can, like the evolution of the electric and magnetic fields!


('I think' being operative here, someone with more experiences with this could answer more clearly and probably more correctly)
 
ok. In what time of application or simply why would we multiply Associated Legendre with another function and then integrate over the real line?
 

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