Mixing
integral of exponential (Green) function with trigonometric variable
$begingroup$
I am searching for a tip on how to handle the following integral,
$int_c^infty exp(-x^2) sin(frac{b}{x^2}) dx$
and also
$int_c^infty exp(-x^2) cos(frac{b}{x^2}) dx$
where both c and b are real. I could not find it in the Integrals table. Thanks for having a look!
integration
asked Feb 3 at 11:20
DT2DT2
1
$endgroup$
add a comment |
$begingroup$
I am searching for a tip on how to handle the following integral,
$int_c^infty exp(-x^2) sin(frac{b}{x^2}) dx$
and also
$int_c^infty exp(-x^2) cos(frac{b}{x^2}) dx$
where both c and b are real. I could not find it in the Integrals table. Thanks for having a look!
integration
asked Feb 3 at 11:20
DT2DT2
1
$endgroup$
$begingroup$
It can expressed by the Error function
$endgroup$
– Dr. Sonnhard Graubner
Feb 3 at 11:25
$begingroup$
The erfc function would in fact be the integral of the first factor, but the cosine or the sine would change that. I did not find an expression for it. Did you?
$endgroup$
– DT2
Feb 3 at 13:58
$begingroup$
You may be interested in the first answer in this question:math.stackexchange.com/questions/128687/…
$endgroup$
– Zachary
Feb 3 at 15:07
add a comment |
$begingroup$
I am searching for a tip on how to handle the following integral,
$int_c^infty exp(-x^2) sin(frac{b}{x^2}) dx$
and also
$int_c^infty exp(-x^2) cos(frac{b}{x^2}) dx$
where both c and b are real. I could not find it in the Integrals table. Thanks for having a look!
integration
asked Feb 3 at 11:20
DT2DT2
1
$endgroup$
I am searching for a tip on how to handle the following integral,
$int_c^infty exp(-x^2) sin(frac{b}{x^2}) dx$
and also
$int_c^infty exp(-x^2) cos(frac{b}{x^2}) dx$
where both c and b are real. I could not find it in the Integrals table. Thanks for having a look!
integration
integration
asked Feb 3 at 11:20
DT2DT2
1
asked Feb 3 at 11:20
DT2DT2
1
asked Feb 3 at 11:20
DT2DT2
1
asked Feb 3 at 11:20
DT2DT2
1
asked Feb 3 at 11:20
DT2DT2
1
1
$begingroup$
It can expressed by the Error function
$endgroup$
– Dr. Sonnhard Graubner
Feb 3 at 11:25
$begingroup$
The erfc function would in fact be the integral of the first factor, but the cosine or the sine would change that. I did not find an expression for it. Did you?
$endgroup$
– DT2
Feb 3 at 13:58
$begingroup$
You may be interested in the first answer in this question:math.stackexchange.com/questions/128687/…
$endgroup$
– Zachary
Feb 3 at 15:07
add a comment |
$begingroup$
It can expressed by the Error function
$endgroup$
– Dr. Sonnhard Graubner
Feb 3 at 11:25
$begingroup$
The erfc function would in fact be the integral of the first factor, but the cosine or the sine would change that. I did not find an expression for it. Did you?
$endgroup$
– DT2
Feb 3 at 13:58
$begingroup$
You may be interested in the first answer in this question:math.stackexchange.com/questions/128687/…
$endgroup$
– Zachary
Feb 3 at 15:07
$begingroup$
It can expressed by the Error function
$endgroup$
– Dr. Sonnhard Graubner
Feb 3 at 11:25
$begingroup$
It can expressed by the Error function
$endgroup$
– Dr. Sonnhard Graubner
Feb 3 at 11:25
$begingroup$
The erfc function would in fact be the integral of the first factor, but the cosine or the sine would change that. I did not find an expression for it. Did you?
$endgroup$
– DT2
Feb 3 at 13:58
$begingroup$
The erfc function would in fact be the integral of the first factor, but the cosine or the sine would change that. I did not find an expression for it. Did you?
$endgroup$
– DT2
Feb 3 at 13:58
$begingroup$
You may be interested in the first answer in this question:math.stackexchange.com/questions/128687/…
$endgroup$
– Zachary
Feb 3 at 15:07
$begingroup$
You may be interested in the first answer in this question:math.stackexchange.com/questions/128687/…
$endgroup$
– Zachary
Feb 3 at 15:07
add a comment |
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$begingroup$
It can expressed by the Error function
$endgroup$
– Dr. Sonnhard Graubner
Feb 3 at 11:25
$begingroup$
The erfc function would in fact be the integral of the first factor, but the cosine or the sine would change that. I did not find an expression for it. Did you?
$endgroup$
– DT2
Feb 3 at 13:58
$begingroup$
You may be interested in the first answer in this question:math.stackexchange.com/questions/128687/…
$endgroup$
– Zachary
Feb 3 at 15:07