How do you solve $int_0^-inftyJ_0(br)e^iasqrtf_0^2-r^2rdr$
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How is solved this integral of Bessel function ?
$$int_0^-inftyJ_0(br)e^iasqrtf_0^2-r^2rdr$$
where $a, b$ are real numbers, $f_0>r$
integration transformation
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up vote
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How is solved this integral of Bessel function ?
$$int_0^-inftyJ_0(br)e^iasqrtf_0^2-r^2rdr$$
where $a, b$ are real numbers, $f_0>r$
integration transformation
Looks like a Hankel Transform. Maybe the corresponding 2D Fourier-Transform is easier ... ? Otherwise you may expand the Bessel Function in a power-series and then integrate. Also make sure to check out common intagral-tables, e.g. Gradshteyn Ryzhick. Finally: is $e^i a sqrtf_0^2-r^2 in L^1(]0,infty[)$?
â denklo
Sep 7 at 10:06
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up vote
0
down vote
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up vote
0
down vote
favorite
How is solved this integral of Bessel function ?
$$int_0^-inftyJ_0(br)e^iasqrtf_0^2-r^2rdr$$
where $a, b$ are real numbers, $f_0>r$
integration transformation
How is solved this integral of Bessel function ?
$$int_0^-inftyJ_0(br)e^iasqrtf_0^2-r^2rdr$$
where $a, b$ are real numbers, $f_0>r$
integration transformation
integration transformation
edited Sep 7 at 9:57
Bernard
112k635104
112k635104
asked Sep 7 at 9:47
ole
153
153
Looks like a Hankel Transform. Maybe the corresponding 2D Fourier-Transform is easier ... ? Otherwise you may expand the Bessel Function in a power-series and then integrate. Also make sure to check out common intagral-tables, e.g. Gradshteyn Ryzhick. Finally: is $e^i a sqrtf_0^2-r^2 in L^1(]0,infty[)$?
â denklo
Sep 7 at 10:06
add a comment |Â
Looks like a Hankel Transform. Maybe the corresponding 2D Fourier-Transform is easier ... ? Otherwise you may expand the Bessel Function in a power-series and then integrate. Also make sure to check out common intagral-tables, e.g. Gradshteyn Ryzhick. Finally: is $e^i a sqrtf_0^2-r^2 in L^1(]0,infty[)$?
â denklo
Sep 7 at 10:06
Looks like a Hankel Transform. Maybe the corresponding 2D Fourier-Transform is easier ... ? Otherwise you may expand the Bessel Function in a power-series and then integrate. Also make sure to check out common intagral-tables, e.g. Gradshteyn Ryzhick. Finally: is $e^i a sqrtf_0^2-r^2 in L^1(]0,infty[)$?
â denklo
Sep 7 at 10:06
Looks like a Hankel Transform. Maybe the corresponding 2D Fourier-Transform is easier ... ? Otherwise you may expand the Bessel Function in a power-series and then integrate. Also make sure to check out common intagral-tables, e.g. Gradshteyn Ryzhick. Finally: is $e^i a sqrtf_0^2-r^2 in L^1(]0,infty[)$?
â denklo
Sep 7 at 10:06
add a comment |Â
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Looks like a Hankel Transform. Maybe the corresponding 2D Fourier-Transform is easier ... ? Otherwise you may expand the Bessel Function in a power-series and then integrate. Also make sure to check out common intagral-tables, e.g. Gradshteyn Ryzhick. Finally: is $e^i a sqrtf_0^2-r^2 in L^1(]0,infty[)$?
â denklo
Sep 7 at 10:06