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惠特克函数

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惠特克函数

我怎样才能绘制 Whittaker 函数；我的意思是代码是什么？

我尝试了以下方法：

\documentclass{article}

\usepackage{mpmath}

\usepackage{tikz}

\usepackage{pgfplots}


\begin{document}

\begin{tikzpicture}

\begin{axis}[xlabel=$x$,ylabel=$y$,
xmin=-2,xmax=2,ymin=0,ymax=0.5, axis lines=center, axis equal]

\addplot[ color=blue,]{Whitw[1, x, 10], {x, -100, 0}};

\end{axis}

\end{tikzpicture}

\end{document}

答案1

我认为在 TeX 中计算 Witteker 函数的结果不太合理。但你可以用一些外部程序（例如 Python 程序）生成数据我已经做好了），然后使用 TikZ 进行绘图。

\documentclass[tikz,border=7pt]{standalone}
\usepackage{pgfplots}
\begin{document}
  \begin{tikzpicture}
    \begin{semilogyaxis}
      % data generated with iPython : https://colab.research.google.com/gist/kpym/41d4723d06bec948638602fd7f6922c0/whittakerw-for-tikz.ipynb
      \addplot coordinates {(-100.0,1.31E+118) (-99.0,3.28E+116) (-98.0,8.29E+114) (-97.0,2.12E+113) (-96.0,5.45E+111) (-95.0,1.42E+110) (-94.0,3.73E+108) (-93.0,9.93E+106) (-92.0,2.67E+105) (-91.0,7.25E+103) (-90.0,1.99E+102) (-89.0,5.53E+100) (-88.0,1.55E+99) (-87.0,4.41E+97) (-86.0,1.27E+96) (-85.0,3.68E+94) (-84.0,1.08E+93) (-83.0,3.22E+91) (-82.0,9.70E+89) (-81.0,2.96E+88) (-80.0,9.12E+86) (-79.0,2.85E+85) (-78.0,9.02E+83) (-77.0,2.89E+82) (-76.0,9.38E+80) (-75.0,3.08E+79) (-74.0,1.03E+78) (-73.0,3.47E+76) (-72.0,1.19E+75) (-71.0,4.12E+73) (-70.0,1.45E+72) (-69.0,5.18E+70) (-68.0,1.88E+69) (-67.0,6.90E+67) (-66.0,2.57E+66) (-65.0,9.74E+64) (-64.0,3.74E+63) (-63.0,1.46E+62) (-62.0,5.80E+60) (-61.0,2.34E+59) (-60.0,9.57E+57) (-59.0,3.99E+56) (-58.0,1.69E+55) (-57.0,7.27E+53) (-56.0,3.19E+52) (-55.0,1.42E+51) (-54.0,6.46E+49) (-53.0,2.99E+48) (-52.0,1.41E+47) (-51.0,6.77E+45) (-50.0,3.32E+44) (-49.0,1.66E+43) (-48.0,8.45E+41) (-47.0,4.39E+40) (-46.0,2.34E+39) (-45.0,1.27E+38) (-44.0,7.04E+36) (-43.0,4.00E+35) (-42.0,2.32E+34) (-41.0,1.38E+33) (-40.0,8.40E+31) (-39.0,5.24E+30) (-38.0,3.36E+29) (-37.0,2.21E+28) (-36.0,1.49E+27) (-35.0,1.03E+26) (-34.0,7.36E+24) (-33.0,5.40E+23) (-32.0,4.08E+22) (-31.0,3.18E+21) (-30.0,2.56E+20) (-29.0,2.13E+19) (-28.0,1.83E+18) (-27.0,1.63E+17) (-26.0,1.51E+16) (-25.0,1.44E+15) (-24.0,1.44E+14) (-23.0,1.49E+13) (-22.0,1.62E+12) (-21.0,1.83E+11) (-20.0,2.17E+10) (-19.0,2.69E+09) (-18.0,3.52E+08) (-17.0,4.85E+07) (-16.0,7.08E+06) (-15.0,1.10E+06) (-14.0,1.81E+05) (-13.0,3.19E+04) (-12.0,6.04E+03) (-11.0,1.24E+03) (-10.0,2.75E+02) (-9.0,6.69E+01) (-8.0,1.80E+01) (-7.0,5.36E+00) (-6.0,1.80E+00) (-5.0,6.90E-01) (-4.0,3.05E-01) (-3.0,1.58E-01) (-2.0,9.76E-02) (-1.0,7.26E-02)};
    \end{semilogyaxis}
  \end{tikzpicture}
\end{document}

在此处输入图片描述

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