- #1
baby_1
- 159
- 16
Homework Statement
Here is my question
Homework Equations
I don't know with what formula does the book find Fourier series?
Fourier Series in cylindrical coordinate
- Thread starter baby_1
- Start date
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Homework Help Overview
The discussion revolves around the application of Fourier series in cylindrical coordinates, specifically seeking the main formula for deriving the Fourier series in this context.
Discussion Character
- Exploratory, Conceptual clarification
Approaches and Questions Raised
- The original poster expresses uncertainty about the formula used for Fourier series in cylindrical coordinates, contrasting it with their familiarity with Cartesian coordinates. Some participants inquire about the expression for current and suggest exploring the Fourier-Bessel series.
Discussion Status
Participants are actively discussing the formulation of Fourier series in cylindrical coordinates, with some providing general forms of the Fourier-Bessel series. There is an ongoing exploration of the topic, with no explicit consensus reached yet.
Contextual Notes
The original poster indicates a lack of familiarity with the specific formulas for cylindrical coordinates, which may influence their understanding and approach to the problem.
Here is my question
I don't know with what formula does the book find Fourier series?
- #2
deskswirl
- 129
- 50
Have you tried writing an expression for the current?
- #3
baby_1
- 159
- 16
Hello deskswirl
Yes , But I know the Fourier series for 2-dimensional in cartesian coordinate not cylindrical Fourier series.I can do and follow the math procedures.I want to know the main formula that I can derive above equation.
Yes , But I know the Fourier series for 2-dimensional in cartesian coordinate not cylindrical Fourier series.I can do and follow the math procedures.I want to know the main formula that I can derive above equation.
- #4
deskswirl
- 129
- 50
One of the most general forms for the Fourier-Bessel series is given by:
$$\sum\limits_{q}{\sum\limits_{p}{\left\{ \begin{matrix} {{J}_{p}}\left( qr \right) \\ {{Y}_{p}}\left( qr \right)\\\end{matrix} \right\}\left\{ \begin{matrix}
\sin \left( p\phi \right) \\ \cos (p\phi ) \\\end{matrix} \right\}\left\{ \begin{matrix} {{e}^{qz}} \\ {{e}^{-qz}} \\\end{matrix} \right\}}}$$
Another is found by letting $$q\to iq$$ in the above expression. These are the two primary solutions of Laplace's equation in circular-cylinder coordinates. Typically due to the symmetry of the problem in phi or z the expression becomes simpler.
$$\sum\limits_{q}{\sum\limits_{p}{\left\{ \begin{matrix} {{J}_{p}}\left( qr \right) \\ {{Y}_{p}}\left( qr \right)\\\end{matrix} \right\}\left\{ \begin{matrix}
\sin \left( p\phi \right) \\ \cos (p\phi ) \\\end{matrix} \right\}\left\{ \begin{matrix} {{e}^{qz}} \\ {{e}^{-qz}} \\\end{matrix} \right\}}}$$
Another is found by letting $$q\to iq$$ in the above expression. These are the two primary solutions of Laplace's equation in circular-cylinder coordinates. Typically due to the symmetry of the problem in phi or z the expression becomes simpler.
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