polynomial.legendre.
legval2d
在点（x，y）处计算二维勒让德级数。
此函数返回值：
System Message: WARNING/2 (P（x，y）=\和i，j c i，j * L_i(x) * LYJ（Y）)
latex exited with error [stdout] This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2019/dev/Debian) (preloaded format=latex) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2018-12-01> (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls Document Class: article 2018/09/03 v1.4i Standard LaTeX document class (/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?' option. (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty)) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty)) (/usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty)) (/usr/share/texlive/texmf-dist/tex/latex/anyfontsize/anyfontsize.sty) (/usr/share/texlive/texmf-dist/tex/latex/tools/bm.sty) (./math.aux) (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd) (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd) ! Package inputenc Error: Unicode character （ (U+FF08) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Unicode character ， (U+FF0C) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Unicode character ） (U+FF09) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Undefined control sequence. <argument> ...it@tag \begin {split}P（x，y）=\� ��i，j c i，j * L_i(x) *... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Invalid UTF-8 byte "92. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Invalid UTF-8 byte "8C. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Unicode character ， (U+FF0C) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Unicode character ， (U+FF0C) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Unicode character （ (U+FF08) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Unicode character ） (U+FF09) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Unicode character （ (U+FF08) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Unicode character ， (U+FF0C) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Unicode character ） (U+FF09) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Undefined control sequence. <argument> ...it@tag \begin {split}P（x，y）=\� ��i，j c i，j * L_i(x) *... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Invalid UTF-8 byte "92. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Invalid UTF-8 byte "8C. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Unicode character ， (U+FF0C) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Unicode character ， (U+FF0C) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Unicode character （ (U+FF08) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} ! Package inputenc Error: Unicode character ） (U+FF09) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...j c i，j * L_i(x) * LYJ（Y）\end{split} [1] (./math.aux) ) (see the transcript file for additional information) Output written on math.dvi (1 page, 436 bytes). Transcript written on math.log.
参数 x 和 y 仅当它们是元组或列表时才转换为数组，否则它们将被视为标量，并且在转换后它们必须具有相同的形状。在任何一种情况下，要么 x 和 y 或者它们的元素必须同时支持自身和元素的乘法和加法。 c .
如果 c 是一个一维数组，在其形状上隐式附加一个数组，使其成为二维数组。结果的形状将是c.shape。 [2:] +X.形状。
二维级数是在点上计算的。 (x, y) 在哪里 x 和 y 必须具有相同的形状。如果 x 或 y 是一个列表或元组，它首先被转换为一个ndarray，否则它将保持不变，如果它不是一个ndarray，它将被视为一个标量。
有序排列的系数数组，使多阶i，j项的系数包含在 c[i,j] .如果 c 维度大于两个，其余索引枚举多组系数。
c[i,j]
二维勒让德级数在由对应值对形成的点上的值 x 和 y .
参见
legval
leggrid2d
legval3d
leggrid3d
笔记
1.7.0 新版功能.