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M_1
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Is it possible to express (cos([itex]\theta[/itex])sin([itex]\theta[/itex]))^2 in terms of spherical harmonics?
M_1 said:Is it possible to express (cos([itex]\theta[/itex])sin([itex]\theta[/itex]))^2 in terms of spherical harmonics?
Telling us what you need this for will help us help you.M_1 said:I need an a linear expansion in only spherical harmonics (not combined with trigonometric functions).
Spherical harmonics are a set of mathematical functions that are used to represent complex periodic functions on the surface of a sphere. They are commonly used in the fields of mathematics, physics, and engineering.
Spherical harmonics are closely related to trigonometric functions because they are composed of a combination of sine and cosine functions. However, unlike trigonometric functions, they are defined on a sphere rather than a plane.
Expanding trigonometric functions in spherical harmonics allows us to represent these functions in a more compact and efficient form. It also allows for easier manipulation and calculation of these functions, particularly in the context of spherical geometry.
Spherical harmonics have a wide range of applications, including in physics, astronomy, satellite communications, and geodesy. They are used to model and analyze complex periodic phenomena on the surface of a sphere, such as gravitational fields, electromagnetic radiation, and magnetic fields.
While spherical harmonics are a powerful tool for representing trigonometric functions, they do have some limitations. They are typically only applicable to functions that are periodic on the surface of a sphere, and may not accurately represent functions with high-frequency components or sharp changes in amplitude.