📝 题目
4.3.3 给定零阶贝塞尔函数:
$$ y = {\mathrm{J}}_{0}\left( x\right) = 1 + \mathop{\sum }\limits_{{n = 1}}^{\infty }{\left( -1\right) }^{n}\frac{{x}^{2n}}{{\left( n!\right) }^{2}{2}^{2n}}. $$
求证: 它在实轴上满足方程:
$$ x{y}^{\prime \prime } + {y}^{\prime } + {xy} =
4.3.3 给定零阶贝塞尔函数:
$$ y = {\mathrm{J}}_{0}\left( x\right) = 1 + \mathop{\sum }\limits_{{n = 1}}^{\infty }{\left( -1\right) }^{n}\frac{{x}^{2n}}{{\left( n!\right) }^{2}{2}^{2n}}. $$
求证: 它在实轴上满足方程:
$$ x{y}^{\prime \prime } + {y}^{\prime } + {xy} =