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bessel_function [2016/04/13 15:54] nikolaj created |
bessel_function [2016/04/13 15:54] nikolaj |
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| ==== Function ==== | ==== Function ==== | ||
| | @#FF9944: definition | @#FF9944: $J_{}: ?\to ?$ | | | @#FF9944: definition | @#FF9944: $J_{}: ?\to ?$ | | ||
| - | | @#FF9944: definition | @#FF9944: $J_\alpha(x) := \sum_{m=0}^\infty \dfrac{1}{\Gamma(m+0+1)\Gamma(m+\alpha+1)} (-1)^m{\left(\dfrac{x}{2}\right)}^{2m+\alpha}$ | | + | | @#FF9944: definition | @#FF9944: $J_\alpha(x) := \sum_{m=0}^\infty \dfrac{1}{\Gamma(m+0+1)\,\Gamma(m+\alpha+1)} (-1)^m{\left(\dfrac{x}{2}\right)}^{2m+\alpha}$ | |
| ----- | ----- | ||
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| They solve | They solve | ||
| - | $x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + (x^2 - \alpha^2)y = 0$ | + | $x^2 \dfrac{d^2 y}{dx^2} + x \dfrac{dy}{dx} + (x^2 - \alpha^2)y = 0$ |
| === Theorems === | === Theorems === | ||
