What are the bessel functions at k=0

Thread starter boddhisattva
Start date Oct 18, 2013
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Bessel Bessel functions Functions

In summary, Bessel functions are special functions named after Friedrich Bessel that are used to solve differential equations in mathematics and physics. When k=0, they reduce to sine and cosine functions, making them easy to integrate and manipulate. They are closely related to cylindrical coordinates and have applications in heat conduction, wave propagation, quantum mechanics, signal processing, and image processing. Real-world examples include the vibration of a circular drum, sound waves in a cylindrical pipe, and electric fields around a wire, as well as their role in black holes and DNA analysis.

Oct 18, 2013

boddhisattva

Hi,

Can anybody gives me the value of J0(r) and Y0(r) ?

Thanks

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Oct 19, 2013

UltrafastPED

Science Advisor

Gold Member

Try Wolfram|Alpha for mathematical details like this.

http://mathworld.wolfram.com/BesselFunctionZeros.html
http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html

Related to What are the bessel functions at k=0

1. What are Bessel functions?

Bessel functions are a type of special functions that arise in many different areas of mathematics and physics. They are named after the German mathematician Friedrich Bessel and are used to solve a wide range of differential equations.

2. What is the significance of k=0 in Bessel functions?

When k=0, the Bessel functions reduce to the well-known sine and cosine functions. This is significant because it allows us to easily integrate and manipulate Bessel functions in mathematical calculations.

3. How are Bessel functions related to cylindrical coordinates?

Bessel functions are closely related to cylindrical coordinates, which are a type of coordinate system used to describe points in three-dimensional space. Bessel functions are often used to solve problems involving cylindrical symmetry, such as those found in electromagnetism and fluid dynamics.

4. What are the applications of Bessel functions?

Bessel functions have a wide range of applications in mathematics, physics, and engineering. They are commonly used to solve problems in heat conduction, wave propagation, and quantum mechanics. They are also used in signal processing, image processing, and other areas of science and technology.

5. Are there any real-world examples of Bessel functions?

Yes, there are many real-world examples of Bessel functions. Some common examples include the vibration of a circular drum head, the propagation of sound waves in a cylindrical pipe, and the electric field around a long, thin wire. Bessel functions also play a role in the behavior of black holes and in the analysis of DNA sequences.