Integration of $int_0^lint_0 ^2pi frac exp (i ksqrt (r^2+r (vt) sin phi))r^2 + r (vt) sin phi+d^2 , r ,dr , dphi$.

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I have faced some difficulties to do the following integral



$$int_0^lint_0 ^2pi frac exp (i k sqrt(r^2 + r vt sin phi))r^2 + r vt sin phi +d^2 , r ,dr , dphi$$



Where, $vt$ and $d$ is a constant and its dimension is that of $r$ and $r$ varies from $0$ to $l$.



while trying to understand some cases related to Fresnel diffraction.



Actually, I am not connected to any Institution and trying to continue study taking help from internet or other students. If you kindly give me some hint or text such that on going through which I can do it by myself.



Or would anyone kindly show me the necessary input language for Mathematica to find out the analytical form of the desired answer of the above integration.



Thanking you.




integration special-functions bessel-functions mathematica




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  • Thanks for editing.
    – R. Bhattacharya
    Aug 17 at 8:43










  • I have a similar problem. My integral is something like that: $$ int_0^pi/2fraccos(acos x)1+b sin^2x dx$$
    – Dinesh Shankar
    Aug 17 at 12:30










  • Thanks for editing again.
    – R. Bhattacharya
    Aug 18 at 4:16














up vote
1
down vote

favorite
1












I have faced some difficulties to do the following integral



$$int_0^lint_0 ^2pi frac exp (i k sqrt(r^2 + r vt sin phi))r^2 + r vt sin phi +d^2 , r ,dr , dphi$$



Where, $vt$ and $d$ is a constant and its dimension is that of $r$ and $r$ varies from $0$ to $l$.



while trying to understand some cases related to Fresnel diffraction.



Actually, I am not connected to any Institution and trying to continue study taking help from internet or other students. If you kindly give me some hint or text such that on going through which I can do it by myself.



Or would anyone kindly show me the necessary input language for Mathematica to find out the analytical form of the desired answer of the above integration.



Thanking you.




integration special-functions bessel-functions mathematica




share|cite|improve this question






















  • Thanks for editing.
    – R. Bhattacharya
    Aug 17 at 8:43










  • I have a similar problem. My integral is something like that: $$ int_0^pi/2fraccos(acos x)1+b sin^2x dx$$
    – Dinesh Shankar
    Aug 17 at 12:30










  • Thanks for editing again.
    – R. Bhattacharya
    Aug 18 at 4:16












up vote
1
down vote

favorite
1









up vote
1
down vote

favorite
1






1





I have faced some difficulties to do the following integral



$$int_0^lint_0 ^2pi frac exp (i k sqrt(r^2 + r vt sin phi))r^2 + r vt sin phi +d^2 , r ,dr , dphi$$



Where, $vt$ and $d$ is a constant and its dimension is that of $r$ and $r$ varies from $0$ to $l$.



while trying to understand some cases related to Fresnel diffraction.



Actually, I am not connected to any Institution and trying to continue study taking help from internet or other students. If you kindly give me some hint or text such that on going through which I can do it by myself.



Or would anyone kindly show me the necessary input language for Mathematica to find out the analytical form of the desired answer of the above integration.



Thanking you.




integration special-functions bessel-functions mathematica




share|cite|improve this question














I have faced some difficulties to do the following integral



$$int_0^lint_0 ^2pi frac exp (i k sqrt(r^2 + r vt sin phi))r^2 + r vt sin phi +d^2 , r ,dr , dphi$$



Where, $vt$ and $d$ is a constant and its dimension is that of $r$ and $r$ varies from $0$ to $l$.



while trying to understand some cases related to Fresnel diffraction.



Actually, I am not connected to any Institution and trying to continue study taking help from internet or other students. If you kindly give me some hint or text such that on going through which I can do it by myself.



Or would anyone kindly show me the necessary input language for Mathematica to find out the analytical form of the desired answer of the above integration.



Thanking you.





integration special-functions bessel-functions mathematica





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 22 at 6:07

























asked Aug 17 at 7:13









R. Bhattacharya

63




63











  • Thanks for editing.
    – R. Bhattacharya
    Aug 17 at 8:43










  • I have a similar problem. My integral is something like that: $$ int_0^pi/2fraccos(acos x)1+b sin^2x dx$$
    – Dinesh Shankar
    Aug 17 at 12:30










  • Thanks for editing again.
    – R. Bhattacharya
    Aug 18 at 4:16
















  • Thanks for editing.
    – R. Bhattacharya
    Aug 17 at 8:43










  • I have a similar problem. My integral is something like that: $$ int_0^pi/2fraccos(acos x)1+b sin^2x dx$$
    – Dinesh Shankar
    Aug 17 at 12:30










  • Thanks for editing again.
    – R. Bhattacharya
    Aug 18 at 4:16















Thanks for editing.
– R. Bhattacharya
Aug 17 at 8:43




Thanks for editing.
– R. Bhattacharya
Aug 17 at 8:43












I have a similar problem. My integral is something like that: $$ int_0^pi/2fraccos(acos x)1+b sin^2x dx$$
– Dinesh Shankar
Aug 17 at 12:30




I have a similar problem. My integral is something like that: $$ int_0^pi/2fraccos(acos x)1+b sin^2x dx$$
– Dinesh Shankar
Aug 17 at 12:30












Thanks for editing again.
– R. Bhattacharya
Aug 18 at 4:16




Thanks for editing again.
– R. Bhattacharya
Aug 18 at 4:16















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