Spherical Harmonics Homework: Calculate Coeficients & Express Function

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Homework Help Overview

The discussion revolves around the calculation of coefficients and the expression of a function using spherical harmonics. The original poster presents a specific example function, f(theta, phi) = sin(theta), and seeks assistance in this context.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants inquire about the original poster's attempts with the example function and discuss the process of expressing functions in terms of spherical harmonics. There is also a comparison made to expressing functions in terms of Fourier series.

Discussion Status

The discussion is ongoing, with participants encouraging the original poster to share their attempts to facilitate more targeted assistance. There are questions about understanding the basis of spherical harmonics and how to apply them in expressing functions.

Contextual Notes

There is a mention of the use of LaTeX for equation writing, which may indicate a need for clarity in mathematical expressions. The original poster's understanding of the spherical harmonics base is also under scrutiny, suggesting potential gaps in foundational knowledge.

pgerlein
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Homework Statement



Hi! I need help with this. I have to calculate the expression of a function using spherical harmonics. The relevant equations are given below. An example of a function can be f(theta,phi) = sin(theta)... Can you help me to calculate de coeficients and to express the function? Thanks.


Homework Equations



View attachment formulas.doc

The Attempt at a Solution

 
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Hola pgerlein. Welcome to PF:smile:

Why don't you show us what you've tried for your example ([itex]f(\theta,\phi)=sin(\theta)[/itex]) and we'll know how to help you better.

To make equation writing easier, this forum supports LaTeX. You can find an introduction to using it by clicking here
 
I can´t understand the use of this base (spherical harmonics). If I solve the ecuation that gives the coefficients value, how can I express the function in terms of the spherical harmonics?
 
How would you express a function in terms of a Fourier series, for example? Essentially it's the same idea when you write any function in terms of an infinite series of basis functions.
 

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