- #1
besselevil
- 3
- 0
Hi, I am trying to find the following integral of bessel functions, any help would be great:
∫H0(z)2/z dz
Thanks
∫H0(z)2/z dz
Thanks
How to Integrate Bessel Functions Over z?
- Thread starter besselevil
- Start date
In summary, the conversation is about finding the integral of Bessel functions involving H0(z)2/z and H0(z)2/(z-a). The speaker has tried using a resource but did not find the desired result. They mention that a closed form using standard special functions may not exist and suggest using numerical methods instead.
- #2
Jorriss
- 1,083
- 26
http://www.fh-jena.de/~rsh/Forschung/Stoer/besint.pdf
Perhaps this has the one you are looking for.
Perhaps this has the one you are looking for.
- #3
besselevil
- 3
- 0
Thanks but I have tried it and could not find it. Actually I am interested in integrals involving H0(z)2/(z-a) or J0(z)Y0(z)/(z-a)
- #4
JJacquelin
- 801
- 35
The closed form involves very complicated special functions :
http://www.wolframalpha.com/input/?i=integrate+BesselH(0,x)^2*dx/x
If the denominator is (z-a) instead of z, I doubt that a closed form might exist with the standard special functions.
http://www.wolframalpha.com/input/?i=integrate+BesselH(0,x)^2*dx/x
If the denominator is (z-a) instead of z, I doubt that a closed form might exist with the standard special functions.
- #5
besselevil
- 3
- 0
The website is very useful, thanks a lot!
- #6
Mute
Homework Helper
- 1,388
- 12
JJacquelin said:
Yeah, when I run into a Meijer-G function I usually take that as a sign that I want to solve the problem numerically (or, better yet, move on to another problem entirely.
).FAQ: How to Integrate Bessel Functions Over z?
What is an integral Bessel function over z?
An integral Bessel function over z is a mathematical function that is used to solve differential equations in physics and engineering. It is defined as the integral of the Bessel function of the first kind with respect to the variable z.
How is an integral Bessel function over z calculated?
The integral Bessel function over z can be calculated using numerical methods such as the Simpson's rule or the trapezoidal rule. It can also be expressed as a series or an infinite sum.
What is the significance of the integral Bessel function over z?
The integral Bessel function over z is important in many fields of science and engineering, as it is used to solve problems involving wave propagation, heat transfer, and diffusion. It also has applications in signal processing and image processing.
What is the relationship between the integral Bessel function and the ordinary Bessel function?
The integral Bessel function over z is defined as the integral of the ordinary Bessel function of the first kind. The ordinary Bessel function is a special function that is used to describe oscillatory phenomena in physics and engineering.
Are there any applications of the integral Bessel function over z in real life?
Yes, the integral Bessel function over z has many practical applications in areas such as acoustics, electromagnetics, and fluid mechanics. It is commonly used to model the behavior of waves, heat, and diffusion in different materials and systems.