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Svein submitted a new PF Insights post
Further Sums Found Through Fourier Series
Continue reading the Original PF Insights Post.
Further Sums Found Through Fourier Series
Continue reading the Original PF Insights Post.
Further Sums Found Through Fourier Series - Comments
- Insights
- Thread starter Svein
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- Fourier Fourier series Series Sums
In summary, Svein submitted a new PF Insights post titled "Further Sums Found Through Fourier Series" and shared a quick Latex pointer for using parentheses. Mathematica gave a similar result and Svein is satisfied as long as he gets correct answers. However, there is a disagreement on the sign of the last result, with Mathematica being correct.
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kith
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Quick Latex pointer: if you write "\left(" and "\right)" instead of "(" and ")" you get parentheses which self-adjust their height.
- #3
The Electrician
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Mathematica gave this:
Last edited:
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Then Mathematica and I agree. Fine!The Electrician said:
For me this is part of the road I am currently going. As long as I am getting correct answers along the way, I am happy.
- #5
The Electrician
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Svein said:
Did you notice that Mathematica disagrees on the sign of the last one?
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No, saw it just now. Mathematica is correct, the correct exponent for (-1) should be (n-1), not n.The Electrician said:
1. What is the purpose of "Further Sums Found Through Fourier Series"?
The purpose of "Further Sums Found Through Fourier Series" is to explore and analyze the properties and applications of Fourier series, which are mathematical tools used to represent periodic functions as a sum of simple trigonometric functions. This topic is relevant in many fields of science and engineering, such as signal processing, image processing, and quantum mechanics.
2. How do Fourier series relate to other mathematical concepts?
Fourier series are closely related to other mathematical concepts, such as trigonometric functions, complex numbers, and integrals. They also have connections to other areas of mathematics, such as number theory and differential equations. Understanding Fourier series can also provide insights into the properties of functions and their behavior.
3. What makes Fourier series useful in science and engineering?
Fourier series are useful in science and engineering because they allow us to represent complex and irregular functions in terms of simpler trigonometric functions. This makes it easier to analyze and manipulate these functions, and can provide insights into their behavior and properties. Additionally, Fourier series are widely used in many applications, such as signal and image processing, data compression, and solving differential equations.
4. Are there any limitations or drawbacks to using Fourier series?
While Fourier series have many useful applications, they also have some limitations. For example, they can only be used to represent periodic functions, meaning that they cannot be applied to non-periodic functions. Additionally, some functions may require an infinite number of terms in their Fourier series to accurately represent them, which can be computationally expensive.
5. What are some potential future developments in the study of Fourier series?
The study of Fourier series is an ongoing and active area of research, with potential future developments in various directions. Some potential areas of interest include generalizations to higher dimensions, applications to new fields, and improvements in computational techniques for finding Fourier coefficients. Additionally, there may be new insights and applications of Fourier series in emerging technologies, such as quantum computing.
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