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Vadim Winebrand
Vadim Winebrand
  • 91
  • 6

Dear all,
please help me solve the following integral.
I need to solve this integral for one of my problems. $$(\frac{1}{2\pi})^2\int_0^\infty\int_{-\infty}^\infty \frac{J_0(\rho R_0)J_0(\rho r)L*Sinc(\frac{Lk_z}{2})e^{jk_zz}}{(\frac{\omega_0}{c})^2-(\rho^2+k_z^2)}\rho\operatorname{d}k_z\operatorname{d}\rho$$ $J_0(x)$ is first kind bessel function and $Sinc(x)=sinx(x)/x$$Sinc(x)=sin(x)/x$.
Is this integral have an analytical solution?
I tried to solve it with Mathematica and Matlab but they even can not solve the simplest orthogonal equation: $$\int_0^\infty J_0(ux)J_0(vx)x\operatorname{d}x=\frac{1}{u}\delta(u-v)$$

Please help me solve this integral.
Thanks.

Dear all,
please help me solve the following integral.
I need to solve this integral for one of my problems. $$(\frac{1}{2\pi})^2\int_0^\infty\int_{-\infty}^\infty \frac{J_0(\rho R_0)J_0(\rho r)L*Sinc(\frac{Lk_z}{2})e^{jk_zz}}{(\frac{\omega_0}{c})^2-(\rho^2+k_z^2)}\rho\operatorname{d}k_z\operatorname{d}\rho$$ $J_0(x)$ is first kind bessel function and $Sinc(x)=sinx(x)/x$.
Is this integral have an analytical solution?
I tried to solve it with Mathematica and Matlab but they even can not solve the simplest orthogonal equation: $$\int_0^\infty J_0(ux)J_0(vx)x\operatorname{d}x=\frac{1}{u}\delta(u-v)$$

Please help me solve this integral.
Thanks.

Dear all,
please help me solve the following integral.
I need to solve this integral for one of my problems. $$(\frac{1}{2\pi})^2\int_0^\infty\int_{-\infty}^\infty \frac{J_0(\rho R_0)J_0(\rho r)L*Sinc(\frac{Lk_z}{2})e^{jk_zz}}{(\frac{\omega_0}{c})^2-(\rho^2+k_z^2)}\rho\operatorname{d}k_z\operatorname{d}\rho$$ $J_0(x)$ is first kind bessel function and $Sinc(x)=sin(x)/x$.
Is this integral have an analytical solution?
I tried to solve it with Mathematica and Matlab but they even can not solve the simplest orthogonal equation: $$\int_0^\infty J_0(ux)J_0(vx)x\operatorname{d}x=\frac{1}{u}\delta(u-v)$$

Please help me solve this integral.
Thanks.

correction
Source Link
Vadim Winebrand
Vadim Winebrand
  • 91
  • 6

Dear all,
please help me solve the following integral.
I need to solve this integral for one of my problems. $$\frac{L}{2\pi}\int_0^\infty\int_{-\infty}^\infty \frac{J_0(\rho R_0)J_0(\rho r)Sinc(\frac{Lk_z}{2})e^{jk_zz}}{(\frac{\omega_0}{c})^2-(\rho^2+k_z^2)}\rho\operatorname{d}\rho\operatorname{d}k_z$$$$(\frac{1}{2\pi})^2\int_0^\infty\int_{-\infty}^\infty \frac{J_0(\rho R_0)J_0(\rho r)L*Sinc(\frac{Lk_z}{2})e^{jk_zz}}{(\frac{\omega_0}{c})^2-(\rho^2+k_z^2)}\rho\operatorname{d}k_z\operatorname{d}\rho$$ $J_0(x)$ is first kind bessel function and $Sinc(x)=sinx(x)/x$.
Is this integral have an analytical solution?
I tried to solve it with Mathematica and Matlab but they even can not solve the simplest orthogonal equation: $$\int_0^\infty J_0(ux)J_0(vx)x\operatorname{d}x=\frac{1}{u}\delta(u-v)$$

Please help me solve this integral.
Thanks.

Dear all,
please help me solve the following integral.
I need to solve this integral for one of my problems. $$\frac{L}{2\pi}\int_0^\infty\int_{-\infty}^\infty \frac{J_0(\rho R_0)J_0(\rho r)Sinc(\frac{Lk_z}{2})e^{jk_zz}}{(\frac{\omega_0}{c})^2-(\rho^2+k_z^2)}\rho\operatorname{d}\rho\operatorname{d}k_z$$ $J_0(x)$ is first kind bessel function and $Sinc(x)=sinx(x)/x$.
Is this integral have an analytical solution?
I tried to solve it with Mathematica and Matlab but they even can not solve the simplest orthogonal equation: $$\int_0^\infty J_0(ux)J_0(vx)x\operatorname{d}x=\frac{1}{u}\delta(u-v)$$

Please help me solve this integral.
Thanks.

Dear all,
please help me solve the following integral.
I need to solve this integral for one of my problems. $$(\frac{1}{2\pi})^2\int_0^\infty\int_{-\infty}^\infty \frac{J_0(\rho R_0)J_0(\rho r)L*Sinc(\frac{Lk_z}{2})e^{jk_zz}}{(\frac{\omega_0}{c})^2-(\rho^2+k_z^2)}\rho\operatorname{d}k_z\operatorname{d}\rho$$ $J_0(x)$ is first kind bessel function and $Sinc(x)=sinx(x)/x$.
Is this integral have an analytical solution?
I tried to solve it with Mathematica and Matlab but they even can not solve the simplest orthogonal equation: $$\int_0^\infty J_0(ux)J_0(vx)x\operatorname{d}x=\frac{1}{u}\delta(u-v)$$

Please help me solve this integral.
Thanks.

added additional integral sign
Source Link
Vadim Winebrand
Vadim Winebrand
  • 91
  • 6

Dear all,
please help me solve the following integral.
I need to solve this integral for one of my problems. $$\frac{L}{2\pi}\int_0^\infty\frac{J_0(\rho R_0)J_0(\rho r)Sinc(\frac{Lk_z}{2})e^{jk_zz}}{(\frac{\omega_0}{c})^2-(\rho^2+k_z^2)}\rho\operatorname{d}\rho\operatorname{d}k_z$$$$\frac{L}{2\pi}\int_0^\infty\int_{-\infty}^\infty \frac{J_0(\rho R_0)J_0(\rho r)Sinc(\frac{Lk_z}{2})e^{jk_zz}}{(\frac{\omega_0}{c})^2-(\rho^2+k_z^2)}\rho\operatorname{d}\rho\operatorname{d}k_z$$ $J_0(x)$ is first kind bessel function and $Sinc(x)=sinx(x)/x$.
Is this integral have an analytical solution?
I tried to solve it with Mathematica and Matlab but they even can not solve the simplest orthogonal equation: $$\int_0^\infty J_0(ux)J_0(vx)x\operatorname{d}x=\frac{1}{u}\delta(u-v)$$

Please help me solve this integral.
Thanks.

Dear all,
please help me solve the following integral.
I need to solve this integral for one of my problems. $$\frac{L}{2\pi}\int_0^\infty\frac{J_0(\rho R_0)J_0(\rho r)Sinc(\frac{Lk_z}{2})e^{jk_zz}}{(\frac{\omega_0}{c})^2-(\rho^2+k_z^2)}\rho\operatorname{d}\rho\operatorname{d}k_z$$ $J_0(x)$ is first kind bessel function and $Sinc(x)=sinx(x)/x$.
Is this integral have an analytical solution?
I tried to solve it with Mathematica and Matlab but they even can not solve the simplest orthogonal equation: $$\int_0^\infty J_0(ux)J_0(vx)x\operatorname{d}x=\frac{1}{u}\delta(u-v)$$

Please help me solve this integral.
Thanks.

Dear all,
please help me solve the following integral.
I need to solve this integral for one of my problems. $$\frac{L}{2\pi}\int_0^\infty\int_{-\infty}^\infty \frac{J_0(\rho R_0)J_0(\rho r)Sinc(\frac{Lk_z}{2})e^{jk_zz}}{(\frac{\omega_0}{c})^2-(\rho^2+k_z^2)}\rho\operatorname{d}\rho\operatorname{d}k_z$$ $J_0(x)$ is first kind bessel function and $Sinc(x)=sinx(x)/x$.
Is this integral have an analytical solution?
I tried to solve it with Mathematica and Matlab but they even can not solve the simplest orthogonal equation: $$\int_0^\infty J_0(ux)J_0(vx)x\operatorname{d}x=\frac{1}{u}\delta(u-v)$$

Please help me solve this integral.
Thanks.

Source Link
Vadim Winebrand
Vadim Winebrand
  • 91
  • 6