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keisanHigh-precision calculations for everyday life and work

First-Kind Bessel Function (Graph)

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Calculate the table for the first-kind Bessel function Jv(x) and display it as a graph.
Order ν
Real numbers
[ Initial value of x
]
\(\normalsize Bessel\ function\ of\ the\ 1st\ kind\ J_\nu(x)\\ (1)\ x^2y''+xy'+(x^2-\nu^2)y=0\\ \hspace{25px} y=J_\nu(x)\\ (2)\ J_\nu(x)={\large\displaystyle \sum_{\small k=0}^{\small\infty}\frac{(-1)^k}{k!\Gamma(k+\nu+1)}(\frac{x}{2})^{\nu+2k}}\\ (3)\ {\large e^{\frac{x}{2}(t-{\large\frac{1}{t}})}}={\large\displaystyle \sum_{\small n=-\infty}^{\small\infty}}J_n(x)t^n,\hspace{20pt} n=integer\\\)

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