Lesson plan
Struve function
[[File:Mplwp Struve function05.svg|320px|thumb|Graph of \mathrm{H}_n(x) for n\in [0,1,2,3,4,5] In mathematics, the Struve functions , are solutions of the non-homogeneous Bessel's differential equation: : x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + \left (x^2 - \alpha^2 \right )y = \frac{4\left (\frac{x}{2}\right)^{\alpha+1}}{\sqrt{\pi}\Gamma \left (\alpha+\frac{1}{2} \right )} introduced by . The complex number α is the order of the Struve function, and is often an integer. And further defined its second-kind version \mathbf{K}_\alpha(x) as \mathbf{K}_\alpha(x)=\mathbf{H}_\alpha(x)-Y_\alpha(x) , where Y_\alpha(x) is the Neumann function. The modified Struve functions are equal to and are solutions of the non-homogeneous Bessel's differential equation: : x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} - \left (x^2 + \alpha^2 \right )y = \frac{4\left (\frac{x}{2}\right)^{\alpha+1}}{\sqrt{\pi}\Gamma \left (\alpha+\frac{1}{2} \right )} And further defined its second-kind version \mathbf{M}_\alpha(x) as \mathbf{M}_\alpha(x)=\mathbf{L}_\alpha(x)-I_\alpha(x) , where I_\alpha(x) is the modified Bessel function of the first kind.
Article summary
[[File:Mplwp Struve function05.svg|320px|thumb|Graph of \mathrm{H}_n(x) for n\in [0,1,2,3,4,5] In mathematics, the Struve functions , are solutions of the non-homogeneous Bessel's differential equation: : x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + \left (x^2 - \alpha^2 \right )y = \frac{4\left (\frac{x}{2}\right)^{\alpha+1}}{\sqrt{\pi}\Gamma \left (\alpha+\frac{1}{2} \right )} introduced by . The complex number α is the order of the Struve function, and is often an integer. And further defined its second-kind version \mathbf{K}_\alpha(x) as \mathbf{K}_\alpha(x)=\mathbf{H}_\alpha(x)-Y_\alpha(x) , where Y_\alpha(x) is the Neumann function. The modified Struve functions are equal to and are solutions of the non-homogeneous Bessel's differential equation: : x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} - \left (x^2 + \alpha^2 \right )y = \frac{4\left (\frac{x}{2}\right)^{\alpha+1}}{\sqrt{\pi}\Gamma \left (\alpha+\frac{1}{2} \right )} And further defined its second-kind version \mathbf{M}_\alpha(x) as \mathbf{M}_\alpha(x)=\mathbf{L}_\alpha(x)-I_\alpha(x) , where I_\alpha(x) is the modified Bessel function of the first kind.
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Discussion questions
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