連續函數，包括超幾何函數

Question

我怎麼能在 LaTeX 中繪製這個 pdf ？

我做了這個

\documentclass[a4 , 12pt]{article}

\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}

\begin{axis}[
    samples at={-20,...,20},

   ]

\addplot [mark=*, cyan] {{(x^2)^0.5}*hypergeompmf(2,1.5,3,1-x^2)}; 

\end{axis}

\end{tikzpicture}

\end{document}

Answer 1

透過從 得到的數值近似Wolframalpha，

\documentclass{article}
\usepackage{pgfplots}
\begin{document}
%https://www.wolframalpha.com/input/?i=(x%2F8)*Hypergeometric2F1%5B2,3%2F2,+3,+1-x%5E2%5D 
%numerical approximation of your function from WolframAlpha
\[\frac{(x^2)^{\frac{1}{2}}}{8}~_{2}F_{1}(2,\frac{3}{2};3;1-x^2), ~ x\in R\approx-\frac{x(-x^2+2x-1)}{(2x*(x^2-1)^2)}
\]
\begin{tikzpicture}[
declare function={ myfun(\x)  =-x*(-x^2+2*(x)-1)/(2*((x))*(x^2-1)^2)));
                 },
]
\begin{axis}[domain=0.01:10]
% I made a strong assumption that the real-values here includes the 0. But that is only during plotting and not while approximating this function.
\addplot {myfun(x)};
\end{axis}
\end{tikzpicture}


\end{document}

你可以繪製

免責聲明：IMO，這個問題out-of-scope顯然是這個論壇的問題。這將屬於https://math.stackexchange.com/questions。並且，在本網站中，我們只能協助解決TeX相關問題。