Integral of Bessel functions combination?

In summary, the speaker is asking if there is a way to compute the integrals involving Bessel functions, specifically when the Bessel functions are replaced by BesselY. The response is that there is no known closed-form expression for these integrals.
  • #1
aymen10
1
0
I want to ask if you how to compute such integral like:

int(t**2*BesselJ(1,a*t)*BesselJ(1,b*t)*BesselJ(1,c*t), t=1..w)

or

int(t**3*BesselJ(1,a*t)*BesselJ(1,b*t)*BesselJ(1,c*t)*BesselJ(1,d*t), t=1..w)

The same question if any BesselJ is replaced by BesselY.

Thanks
 
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  • #2
aymen10 said:
I want to ask if you how to compute such integral like:

int(t**2*BesselJ(1,a*t)*BesselJ(1,b*t)*BesselJ(1,c*t), t=1..w)

or

int(t**3*BesselJ(1,a*t)*BesselJ(1,b*t)*BesselJ(1,c*t)*BesselJ(1,d*t), t=1..w)

The same question if any BesselJ is replaced by BesselY.

Thanks

I see no reason to think there is a closed-form expression (not involving integrals) for that.
 

1. What is the integral of Bessel functions combination?

The integral of Bessel functions combination is a mathematical expression that represents the area under the curve of a combination of Bessel functions. It is commonly used in engineering and physics to solve problems involving oscillatory systems.

2. How is the integral of Bessel functions combination calculated?

The integral of Bessel functions combination is typically calculated using numerical methods or special functions such as the Meijer G-function. It can also be expressed in terms of other known functions, such as the incomplete gamma function.

3. What are some applications of the integral of Bessel functions combination?

The integral of Bessel functions combination has several applications in physics and engineering, including solving problems related to heat conduction, electromagnetic fields, and quantum mechanics. It is also used in signal processing and image analysis.

4. Are there any special properties of the integral of Bessel functions combination?

Yes, there are several special properties of the integral of Bessel functions combination. One of them is the orthogonality property, which states that the integral of the product of two different Bessel functions is equal to zero. This property is useful in solving certain boundary value problems.

5. Are there any practical tips for evaluating the integral of Bessel functions combination?

When evaluating the integral of Bessel functions combination, it is important to consider the symmetry of the function and make use of known identities and properties. It is also helpful to use software or numerical methods for more complex integrals. Additionally, it is important to carefully check the limits of integration and ensure that the final solution is in the correct units.

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