How can the following integration including modified-Bessel function be calculated?
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I derived the following expression as a solution for the diffusion-convection equation in radial coordinates. I would like to know if this integration can be calculated.
$$int_0^inftyxexpleft(-,x^2 + z^2 over 2sigma^2right)
rm I_vleft(vphantomlarge Axz over sigma^2right),rm dx$$
Where:
$$rm I_v$$
is the modified Bessel function of the first kind with non-integer order (v).
integration improper-integrals bessel-functions
asked Aug 26 at 21:44
Galal
63
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up vote
-1
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I derived the following expression as a solution for the diffusion-convection equation in radial coordinates. I would like to know if this integration can be calculated.
$$int_0^inftyxexpleft(-,x^2 + z^2 over 2sigma^2right)
rm I_vleft(vphantomlarge Axz over sigma^2right),rm dx$$
Where:
$$rm I_v$$
is the modified Bessel function of the first kind with non-integer order (v).
integration improper-integrals bessel-functions
asked Aug 26 at 21:44
Galal
63
If you felt compelled to tag on a $5$ at the end of your title (presumably because the title has already been used without the 5 and maybe even with all of 1,2,3,4 used in place of it as well), then your title is probably not very good or descriptive.
– JMoravitz
Aug 26 at 21:54
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
I derived the following expression as a solution for the diffusion-convection equation in radial coordinates. I would like to know if this integration can be calculated.
$$int_0^inftyxexpleft(-,x^2 + z^2 over 2sigma^2right)
rm I_vleft(vphantomlarge Axz over sigma^2right),rm dx$$
Where:
$$rm I_v$$
is the modified Bessel function of the first kind with non-integer order (v).
integration improper-integrals bessel-functions
asked Aug 26 at 21:44
Galal
63
I derived the following expression as a solution for the diffusion-convection equation in radial coordinates. I would like to know if this integration can be calculated.
$$int_0^inftyxexpleft(-,x^2 + z^2 over 2sigma^2right)
rm I_vleft(vphantomlarge Axz over sigma^2right),rm dx$$
Where:
$$rm I_v$$
is the modified Bessel function of the first kind with non-integer order (v).
integration improper-integrals bessel-functions
asked Aug 26 at 21:44
Galal
63
edited Aug 26 at 22:02
asked Aug 26 at 21:44
Galal
63
asked Aug 26 at 21:44
Galal
63
asked Aug 26 at 21:44
Galal
63
63
If you felt compelled to tag on a $5$ at the end of your title (presumably because the title has already been used without the 5 and maybe even with all of 1,2,3,4 used in place of it as well), then your title is probably not very good or descriptive.
– JMoravitz
Aug 26 at 21:54
add a comment |Â
If you felt compelled to tag on a $5$ at the end of your title (presumably because the title has already been used without the 5 and maybe even with all of 1,2,3,4 used in place of it as well), then your title is probably not very good or descriptive.
– JMoravitz
Aug 26 at 21:54
If you felt compelled to tag on a $5$ at the end of your title (presumably because the title has already been used without the 5 and maybe even with all of 1,2,3,4 used in place of it as well), then your title is probably not very good or descriptive.
– JMoravitz
Aug 26 at 21:54
If you felt compelled to tag on a $5$ at the end of your title (presumably because the title has already been used without the 5 and maybe even with all of 1,2,3,4 used in place of it as well), then your title is probably not very good or descriptive.
– JMoravitz
Aug 26 at 21:54
add a comment |Â
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If you felt compelled to tag on a $5$ at the end of your title (presumably because the title has already been used without the 5 and maybe even with all of 1,2,3,4 used in place of it as well), then your title is probably not very good or descriptive.
– JMoravitz
Aug 26 at 21:54