Kernel of Hankel Transform
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I need to solve a cylindrical diffusion problem that is defined in $[1,infty]$. I would like to use Hankel Transform that has is defined on $[0,infty]$. So in order to apply Hankel transform in my case, do I need to change the Kernel of the Transformation.
calculus differential-equations pde special-functions integral-transforms
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I need to solve a cylindrical diffusion problem that is defined in $[1,infty]$. I would like to use Hankel Transform that has is defined on $[0,infty]$. So in order to apply Hankel transform in my case, do I need to change the Kernel of the Transformation.
calculus differential-equations pde special-functions integral-transforms
You probably have a condition at $r=1$. So your transform should be tailored to that condition.
â DisintegratingByParts
Aug 9 at 17:38
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up vote
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up vote
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down vote
favorite
I need to solve a cylindrical diffusion problem that is defined in $[1,infty]$. I would like to use Hankel Transform that has is defined on $[0,infty]$. So in order to apply Hankel transform in my case, do I need to change the Kernel of the Transformation.
calculus differential-equations pde special-functions integral-transforms
I need to solve a cylindrical diffusion problem that is defined in $[1,infty]$. I would like to use Hankel Transform that has is defined on $[0,infty]$. So in order to apply Hankel transform in my case, do I need to change the Kernel of the Transformation.
calculus differential-equations pde special-functions integral-transforms
edited Aug 8 at 18:42
Javi
2,1711725
2,1711725
asked Aug 8 at 18:07
Three Phi
55
55
You probably have a condition at $r=1$. So your transform should be tailored to that condition.
â DisintegratingByParts
Aug 9 at 17:38
add a comment |Â
You probably have a condition at $r=1$. So your transform should be tailored to that condition.
â DisintegratingByParts
Aug 9 at 17:38
You probably have a condition at $r=1$. So your transform should be tailored to that condition.
â DisintegratingByParts
Aug 9 at 17:38
You probably have a condition at $r=1$. So your transform should be tailored to that condition.
â DisintegratingByParts
Aug 9 at 17:38
add a comment |Â
1 Answer
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Yes, you do.
In general, the Bessel solutions to the boundary value problem require that the function remains finite at r = 0.
If your domain does not include r = 0 (and yours does not!) then you need to use a linear combination of Bessel functions of the first, and second kind.
A bit of Googling will help you to get a good idea about how to go about this. For example, "Theory and Operational Rules for the Discrete Hankel Transform" is a very nice paper which attempts to put the DHT on equal footing with the discrete Fourier transform.
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Yes, you do.
In general, the Bessel solutions to the boundary value problem require that the function remains finite at r = 0.
If your domain does not include r = 0 (and yours does not!) then you need to use a linear combination of Bessel functions of the first, and second kind.
A bit of Googling will help you to get a good idea about how to go about this. For example, "Theory and Operational Rules for the Discrete Hankel Transform" is a very nice paper which attempts to put the DHT on equal footing with the discrete Fourier transform.
add a comment |Â
up vote
1
down vote
Yes, you do.
In general, the Bessel solutions to the boundary value problem require that the function remains finite at r = 0.
If your domain does not include r = 0 (and yours does not!) then you need to use a linear combination of Bessel functions of the first, and second kind.
A bit of Googling will help you to get a good idea about how to go about this. For example, "Theory and Operational Rules for the Discrete Hankel Transform" is a very nice paper which attempts to put the DHT on equal footing with the discrete Fourier transform.
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Yes, you do.
In general, the Bessel solutions to the boundary value problem require that the function remains finite at r = 0.
If your domain does not include r = 0 (and yours does not!) then you need to use a linear combination of Bessel functions of the first, and second kind.
A bit of Googling will help you to get a good idea about how to go about this. For example, "Theory and Operational Rules for the Discrete Hankel Transform" is a very nice paper which attempts to put the DHT on equal footing with the discrete Fourier transform.
Yes, you do.
In general, the Bessel solutions to the boundary value problem require that the function remains finite at r = 0.
If your domain does not include r = 0 (and yours does not!) then you need to use a linear combination of Bessel functions of the first, and second kind.
A bit of Googling will help you to get a good idea about how to go about this. For example, "Theory and Operational Rules for the Discrete Hankel Transform" is a very nice paper which attempts to put the DHT on equal footing with the discrete Fourier transform.
answered Aug 8 at 20:01
user109527
657
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You probably have a condition at $r=1$. So your transform should be tailored to that condition.
â DisintegratingByParts
Aug 9 at 17:38