Mixing
Laplace transform of products of Marcum Q, Bessel J and power functions
$begingroup$
I want to solve this integral likes:
$int_{0}^{infty} Q_{mu_1}left( alpha, betasqrt{t}right) t^{frac{mu_2-1}{2}}J_{mu_2-1} left(csqrt{t}right) exp(-pt)dt$
where $Q(cdot)$ is generalized Marcum-Q function, and $J(cdot)$ is the Bessel function of the first kind. All parameters are real.
I have tried to transform $J$ to $I$ using $I_{nu}(x) = i^{-nu} J_{nu}(ix)$. Then I want to use the reference,
but it not works.
Am I wrong? Can anybody help me to solve this problem?
integration laplace-transform bessel-functions
asked Feb 1 at 7:52
Tianji ShenTianji Shen
11
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add a comment |
$begingroup$
I want to solve this integral likes:
$int_{0}^{infty} Q_{mu_1}left( alpha, betasqrt{t}right) t^{frac{mu_2-1}{2}}J_{mu_2-1} left(csqrt{t}right) exp(-pt)dt$
where $Q(cdot)$ is generalized Marcum-Q function, and $J(cdot)$ is the Bessel function of the first kind. All parameters are real.
I have tried to transform $J$ to $I$ using $I_{nu}(x) = i^{-nu} J_{nu}(ix)$. Then I want to use the reference,
but it not works.
Am I wrong? Can anybody help me to solve this problem?
integration laplace-transform bessel-functions
asked Feb 1 at 7:52
Tianji ShenTianji Shen
11
$endgroup$
add a comment |
$begingroup$
I want to solve this integral likes:
$int_{0}^{infty} Q_{mu_1}left( alpha, betasqrt{t}right) t^{frac{mu_2-1}{2}}J_{mu_2-1} left(csqrt{t}right) exp(-pt)dt$
where $Q(cdot)$ is generalized Marcum-Q function, and $J(cdot)$ is the Bessel function of the first kind. All parameters are real.
I have tried to transform $J$ to $I$ using $I_{nu}(x) = i^{-nu} J_{nu}(ix)$. Then I want to use the reference,
but it not works.
Am I wrong? Can anybody help me to solve this problem?
integration laplace-transform bessel-functions
asked Feb 1 at 7:52
Tianji ShenTianji Shen
11
$endgroup$
I want to solve this integral likes:
$int_{0}^{infty} Q_{mu_1}left( alpha, betasqrt{t}right) t^{frac{mu_2-1}{2}}J_{mu_2-1} left(csqrt{t}right) exp(-pt)dt$
where $Q(cdot)$ is generalized Marcum-Q function, and $J(cdot)$ is the Bessel function of the first kind. All parameters are real.
I have tried to transform $J$ to $I$ using $I_{nu}(x) = i^{-nu} J_{nu}(ix)$. Then I want to use the reference,
but it not works.
Am I wrong? Can anybody help me to solve this problem?
integration laplace-transform bessel-functions
integration laplace-transform bessel-functions
asked Feb 1 at 7:52
Tianji ShenTianji Shen
11
asked Feb 1 at 7:52
Tianji ShenTianji Shen
11
asked Feb 1 at 7:52
Tianji ShenTianji Shen
11
asked Feb 1 at 7:52
Tianji ShenTianji Shen
11
asked Feb 1 at 7:52
Tianji ShenTianji Shen
11
11
add a comment |
add a comment |
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