Why is the first type bessel function called first?

In summary, the difference between first- and second-type Bessel functions lies in their behavior, with the first kind being finite at the origin and the second kind having a singularity there. The numbering convention is simply a way to distinguish between the two classes of solutions for the Bessel equation, with no particular significance attached to the order. For more information, refer to the link provided.
  • #1
wdlang
307
0
what is the difference between first- and second-type bessel functions?
 
Physics news on Phys.org
  • #2
The difference is in the characteristics of their behavior - eg. (and simplistically) the 1st kind are finite at the origin while the 2nd kind have a singularity there for example. So much for the differences - but you also want to know how come the numbering - well, considering these two classes, which one would you like to consider first?

It's a convention. Since the Bessel equation is 2nd order there have to be two independent solutions. I don't think there is anything especially profound about the order.

http://www.springerlink.com/content/rm536p06v8442482/
 

1. Why is the first type Bessel function called "first"?

The term "first" in the first type Bessel function refers to its order, which is the number of times the function is differentiated. In this case, the first type Bessel function is the solution to a differential equation of order one.

2. How is the first type Bessel function different from other types of Bessel functions?

The first type Bessel function, also known as the ordinary Bessel function, is a special case of the more general Bessel function, which has multiple types depending on the form of the differential equation it solves. The first type Bessel function has a specific form that is used to solve problems involving circular, cylindrical, or spherical symmetry.

3. Who first discovered the first type Bessel function?

The first type Bessel function was first studied by mathematician Daniel Bernoulli in the 1730s. However, it was the mathematician Friedrich Bessel who gave the function its name and extensively studied its properties in the 19th century.

4. What are the applications of the first type Bessel function?

The first type Bessel function has many applications in physics and engineering, particularly in problems involving wave phenomena, such as heat transfer, sound, and electromagnetic waves. It is also used in solving problems related to fluid dynamics, diffusion, and image processing.

5. Is there a mathematical formula for the first type Bessel function?

Yes, the first type Bessel function can be expressed as a series of terms involving trigonometric functions and powers of x. The specific formula depends on the order of the function and can be found in many mathematical reference books or online resources.

Similar threads

Replies
2
Views
1K
Replies
2
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
5
Views
1K
Replies
5
Views
1K
Replies
3
Views
2K
Replies
3
Views
1K
  • Differential Equations
Replies
2
Views
2K
Replies
1
Views
821
  • Quantum Physics
Replies
0
Views
535
Back
Top