Modified Bessel Function of the First Kind (Graph)
Calculate and graph the table for the first-kind modified Bessel function Iv(x).
| \(\normalsize Modified\ Bessel\ function\\ \hspace{130px} of\ the\ 1st\ kind\ I_\nu(x)\\ (1)\ x^2y''+xy'-(x^2+\nu^2)y=0\\ \hspace{25px} y=I_\nu(x)\\ (2)\ I_\nu(x)={\large\displaystyle \sum_{\small k=0}^{\small\infty}\frac{1}{k!\Gamma(k+\nu+1)}(\frac{x}{2})^{\nu+2k}}\\ (3)\ {\large e^{\frac{x}{2}(t+{\large\frac{1}{t}})}}={\large\displaystyle \sum_{\small n=-\infty}^{\small\infty}}I_n(x)t^n,\hspace{20px} n=integer\\\) |
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