KRAKENBEAL RECORDS: epubで数式を表現する

[したいこと・しりたいこと・目標]

epubで数式を表示したい
epubにsvgを埋め込みたい
svgで数式を表現したい

[環境]

Ubuntu Jaunty Jackalope 9.04 on VirtualBox 3.1.4
Ubuntu Karmic Koala 9.10 on VMWare Fusion 3
Ubuntu Lucid Lynx 10.04 on VirtualBox 3.1.6
Mac OS X 10.6

[前提]

Ubuntu
sigilとFBReader導入済み

Mac
sigilとAdobe Digital Editions導入済み

[したこと]

(01)epubに埋め込みたい数式のtexソースを書く

taylor1.tex

\documentclass[30pt]{jsarticle}
\usepackage{amsmath}
\begin{document}
\thispagestyle{empty}
$\sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!} (x - a)^{n}$
\end{document}

taylor2.tex

\documentclass[30pt]{jsarticle}
\usepackage{amsmath}
\begin{document}
\thispagestyle{empty}
$f^{(n)} (a)$
\end{document}

taylor3.tex

\documentclass[30pt]{jsarticle}
\usepackage{amsmath}
\begin{document}
\thispagestyle{empty}
$(x-a)^{0}$
\end{document}

(02)変換する

LaTeX の数式を PNG と SVG に変換する - akihiko’s tech note
http://d.hatena.ne.jp/aki-yam/20080924/1222280563
このページ step2 を参考にしてepubに埋め込む数式svgを作成した。

shスクリプトにして、変換してみた（この作業はubuntuで行った)

tex_svg.sh

#!/usr/bin/sh

platex $@.tex
dvipdfmx $@

gs -q -r20480 -sDEVICE=epswrite -sOutputFile=$@.eps -dNOPAUSE -dBATCH -dSAFER -dEPSCrop -dEPSFitPage -dUseCropBox $@.pdf

pstoedit -f plot-svg -dt -ssp -sclip $@.eps | sed 's/<rect[^<>]+id="background"[^<>]*>//g' > $@.svg

使い方　
sh tex_svg.sh taylor
これで
taylor.dvi taylor.pdf taylor.eps taylor.svg
が、得られる

(03)変換した数式のsvgをinkscapeで開いて、調整する

数式オブジェクトを選択する
オブジェクト　変形　拡大縮小　比率を維持して拡大縮小
独立文構造数式100%
文中数式40%
ファイル　ドキュメントの設定　ページを選択ドキュメントにフィット

(04)inkscapeで調整されたsvgを、テキストエディタで開き、内容をsigilに貼り付ける
ただし、１行目の
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
という、宣言文は除く

(05)epubで日本語が表示出きるように、sigilで5行目の宣言を下記のように変更する。
<html xmlns="http://www.w3.org/1999/xhtml" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="ja">

(06)保存して、表示してみる

Adobe Digital Editionsで数式をsvg化したものを埋め込んだ文章を表示

FBReaderで数式をsvg化したものを埋め込んだ文章を表示

[注意]

AdobeDigitalEditionsでは、埋め込んだsvgの数式が表示できる
FBReaderでは埋め込んだsvgの数式が表示できない

svgをテキストエディタで開いたとき
<desc id="desc5"></desc>
タグで囲まれている部分に、tex数式を書き込んでおくとよい。
FBReaderのようなsvgが表示できないepubリーダーで、どんな数式が書いてあるのか、とりあえず分かるようになる。

FBReaderでsvgの数式を表示するには、直接埋め込むのではなく、imageとして挿入する必要がある。
しかし、文中式の表示ができない。
独立した行の中央に表示される。
この方法の問題点は、数式の大きさが固定されてしまう点だ。
直接svgで数式を埋め込む方式なら、数式の大きさが変えられるので、視力に自信が無い人にもやさしい。

掲載したtexソースでは、大きさを30ptにしてある
文中に含める数式に使用するsvgのソースとしてのtexファイルなら12ptの大きさに変更した方が便利だ。inlscape上での作業が減る。

[参考]

LaTeX の数式を PNG と SVG に変換する - akihiko’s tech note
http://d.hatena.ne.jp/aki-yam/20080924/1222280563

[その他]

サンプル taylor.epub のダウンロード
taylor.epub

以下、ソース google doc
taylor_epub_src

<?xml version="1.0"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
    "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">

<html xmlns="http://www.w3.org/1999/xhtml" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="ja">
<head>
  <title></title>

  <title id="title3">SVG drawing</title>

  <title id="title3">SVG drawing</title>

  <title id="title3">SVG drawing</title>
  
<style type="text/css">
g.sgc-3 {font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-opacity:1;stroke-dasharray:none;stroke-dashoffset:0}
  line.sgc-2 {stroke-width:1.18840003}
  path.sgc-1 {fill:#000000;fill-rule:nonzero;stroke-width:0}
</style>
</head>

<body>
  <p>テイラー展開（テイラーてんかい、Taylor expansion）とは、無限回微分可能な関数 f(x) から、テイラー級数（テイラーきゅうすう、Taylor series）と呼ばれる、負冪の項を持たない冪級数を得ることを言う。名称は数学者ブルック・テイラーに由来する。 実数または複素数関数の f(x) が 1 変数関数の場合には<br /></p>

  <svg xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns="http://www.w3.org/2000/svg" xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd" xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:svg="http://www.w3.org/2000/svg" xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape" width="337.76035" version="1.1" preserveAspectRatio="none" height="56.274639" viewBox="0 0 0.46911159 0.078159221" sodipodi:docname="taylor.svg" id="body" inkscape:version="0.47 r22583">
    <metadata id="metadata58">image/svg+xml</metadata>

    <defs id="defs56"></defs>

    <desc id="desc5">sum_{n=0}^{infty} frac{f^{(n)}(a)}{n!} (x - a)^{n}</desc>

    <g xmlns:xml="http://www.w3.org/XML/1998/namespace" class="sgc-3" font-style="normal" word-spacing="normal" id="content" font-weight="normal" xml:space="preserve" font-stretch="normal" letter-spacing="normal" transform="matrix(0.0017361,0,0,-0.0017361,-0.18532868,1.201034)" stroke-miterlimit="10.433" font-variant="normal" font-size-adjust="none">
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  <p><br />
  ここで n! は n の階乗で、</p>

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    <defs id="defs24"></defs>

    <desc id="desc5">f^(n) (a)</desc>

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      <path class="sgc-1" id="path10" d="m 130.24,688.47 -0.36,-0.27 -0.35,-0.28 -0.33,-0.28 -0.31,-0.29 -0.3,-0.3 -0.28,-0.31 -0.27,-0.31 -0.25,-0.32 -0.24,-0.32 -0.22,-0.33 -0.21,-0.33 -0.2,-0.34 -0.18,-0.34 -0.17,-0.34 -0.16,-0.34 -0.15,-0.35 -0.14,-0.35 -0.12,-0.35 -0.11,-0.34 -0.11,-0.35 -0.09,-0.35 -0.08,-0.35 -0.08,-0.34 -0.06,-0.34 -0.06,-0.34 -0.04,-0.33 -0.04,-0.33 -0.03,-0.33 -0.03,-0.32 -0.01,-0.31 -0.01,-0.31 0,-0.31 c 0,-2.93 0.87,-7.49 4.99,-10.41 0.17,0 0.42,0 0.42,0.25 0,0.12 -0.06,0.17 -0.21,0.31 -2.77,2.5 -3.79,6.04 -3.79,9.83 0,5.63 2.14,8.38 3.85,9.92 0.09,0.08 0.15,0.14 0.15,0.25 0,0.25 -0.25,0.25 -0.42,0.25 z"></path>

      <path class="sgc-1" id="path12" d="m 134.68,674.16 -0.01,-0.03 -0.01,-0.03 0,-0.03 -0.01,-0.03 -0.01,-0.03 -0.01,-0.03 -0.01,-0.03 -0.01,-0.03 -0.01,-0.07 -0.02,-0.07 -0.02,-0.06 -0.01,-0.07 -0.01,-0.03 -0.01,-0.03 -0.01,-0.03 0,-0.03 -0.01,-0.03 -0.01,-0.02 0,-0.03 -0.01,-0.02 0,-0.03 0,-0.02 -0.01,-0.02 0,-0.01 0,-0.02 -0.01,-0.01 0,0 0,-0.01 0,0 0,-0.01 c 0,-0.46 0.38,-0.66 0.71,-0.66 0.37,0 0.71,0.27 0.81,0.45 0.1,0.19 0.27,0.86 0.38,1.3 0.1,0.39 0.33,1.35 0.45,1.87 0.13,0.46 0.25,0.92 0.36,1.4 0.23,0.85 0.27,1.02 0.87,1.87 0.59,0.83 1.56,1.92 3.13,1.92 1.2,0 1.23,-1.07 1.23,-1.46 0,-1.25 -0.9,-3.56 -1.23,-4.44 -0.23,-0.58 -0.32,-0.77 -0.32,-1.12 0,-1.11 0.92,-1.79 1.98,-1.79 2.09,0 3,2.87 3,3.18 0,0.27 -0.27,0.27 -0.33,0.27 -0.3,0 -0.31,-0.12 -0.4,-0.35 -0.48,-1.67 -1.37,-2.52 -2.2,-2.52 -0.44,0 -0.53,0.29 -0.53,0.73 0,0.48 0.11,0.75 0.48,1.69 0.25,0.64 1.11,2.85 1.11,4.02 0,2.02 -1.61,2.37 -2.71,2.37 -1.73,0 -2.9,-1.06 -3.52,-1.9 -0.15,1.44 -1.37,1.9 -2.23,1.9 -0.89,0 -1.37,-0.65 -1.64,-1.12 -0.46,-0.78 -0.75,-1.96 -0.75,-2.07 0,-0.27 0.29,-0.27 0.35,-0.27 0.29,0 0.32,0.06 0.46,0.63 0.31,1.23 0.71,2.25 1.52,2.25 0.54,0 0.69,-0.46 0.69,-1.02 0,-0.4 -0.19,-1.17 -0.34,-1.73 -0.14,-0.56 -0.35,-1.42 -0.46,-1.88 z"></path>

      <path class="sgc-1" id="path14" d="m 148.73,688.47 -0.01,0 -0.01,-0.01 -0.02,0 -0.02,0 -0.01,0 -0.02,0 -0.01,0 -0.02,0 -0.02,0 -0.01,0 -0.02,-0.01 -0.02,0 -0.01,0 -0.02,-0.01 -0.02,0 -0.01,-0.01 -0.02,0 -0.01,-0.01 -0.01,-0.01 -0.02,-0.01 -0.01,-0.01 -0.01,-0.01 -0.01,-0.01 -0.01,0 0,-0.01 -0.01,-0.01 0,0 -0.01,-0.01 0,-0.01 0,-0.01 -0.01,-0.01 0,0 0,-0.01 -0.01,-0.01 0,-0.01 0,-0.01 0,-0.01 0,-0.01 0,-0.01 0,-0.01 0,-0.01 c 0,-0.11 0.06,-0.17 0.18,-0.32 1.8,-1.64 3.79,-4.45 3.79,-9.83 0,-4.35 -1.35,-7.64 -3.6,-9.68 -0.35,-0.36 -0.37,-0.37 -0.37,-0.48 0,-0.1 0.06,-0.25 0.27,-0.25 0.25,0 2.23,1.37 3.6,3.98 0.91,1.73 1.52,3.98 1.52,6.41 0,2.94 -0.88,7.5 -5,10.42 z"></path>

      <path class="sgc-1" id="path16" d="m 167.48,654.93 0,0.01 0,0.02 0,0.01 0,0.01 0,0.01 0,0.01 -0.01,0.01 0,0.01 -0.01,0.01 0,0.01 -0.01,0.01 -0.01,0.02 -0.01,0.01 -0.01,0.02 -0.01,0.01 -0.02,0.02 -0.01,0.02 -0.02,0.02 -0.01,0.02 -0.01,0.01 -0.01,0.01 -0.01,0.01 -0.01,0.02 -0.01,0.01 -0.02,0.01 -0.01,0.02 -0.01,0.01 -0.02,0.02 -0.01,0.01 -0.02,0.02 -0.01,0.02 -0.02,0.01 -0.02,0.02 -0.01,0.02 -0.02,0.02 -0.02,0.02 -0.02,0.02 -0.02,0.02 -0.02,0.02 -0.02,0.03 -0.03,0.02 -0.02,0.02 c -3.72,3.75 -4.67,9.37 -4.67,13.92 0,5.18 1.13,10.35 4.79,14.07 0.38,0.36 0.38,0.42 0.38,0.51 0,0.21 -0.11,0.3 -0.29,0.3 -0.3,0 -2.98,-2.03 -4.73,-5.8 -1.52,-3.28 -1.88,-6.58 -1.88,-9.08 0,-2.32 0.33,-5.92 1.97,-9.28 1.78,-3.66 4.34,-5.59 4.64,-5.59 0.18,0 0.29,0.09 0.29,0.3 z"></path>

      <path class="sgc-1" id="path18" d="m 180.29,673.31 -0.05,0.1 -0.06,0.11 -0.05,0.09 -0.06,0.1 -0.06,0.09 -0.06,0.1 -0.06,0.09 -0.07,0.08 -0.06,0.09 -0.07,0.08 -0.07,0.08 -0.08,0.08 -0.08,0.07 -0.07,0.08 -0.08,0.06 -0.09,0.07 -0.08,0.06 -0.09,0.06 -0.09,0.05 -0.09,0.06 -0.1,0.04 -0.1,0.05 -0.1,0.04 -0.1,0.04 -0.1,0.03 -0.11,0.03 -0.11,0.02 -0.12,0.02 -0.11,0.02 -0.12,0.01 -0.12,0.01 -0.13,0 c -3.48,0 -7.17,-4.38 -7.17,-8.72 0,-2.8 1.64,-4.76 3.96,-4.76 l 0.06,0.66 c -1.49,0 -1.9,1.63 -1.9,2.79 0,1.49 0.95,5.15 1.63,6.52 0.92,1.75 2.26,2.85 3.45,2.85 1.94,0 2.35,-2.44 2.35,-2.61 0,-0.18 -0.05,-0.36 -0.09,-0.51 l -1.49,-5.84 c -0.14,-0.53 -0.14,-0.59 -0.59,-1.09 -1.31,-1.64 -2.53,-2.11 -3.36,-2.11 l -0.06,-0.66 c 0.59,0 2.08,0.12 3.87,2.23 0.24,-1.25 1.28,-2.23 2.7,-2.23 1.05,0 1.73,0.69 2.21,1.64 0.5,1.07 0.89,2.88 0.89,2.94 0,0.3 -0.27,0.3 -0.36,0.3 -0.3,0 -0.33,-0.12 -0.42,-0.53 -0.5,-1.94 -1.03,-3.69 -2.26,-3.69 -0.8,0 -0.89,0.77 -0.89,1.37 0,0.65 0.06,0.89 0.39,2.2 0.33,1.25 0.38,1.54 0.65,2.68 l 1.08,4.16 c 0.2,0.83 0.2,0.89 0.2,1.01 0,0.5 -0.35,0.8 -0.86,0.8 -0.72,0 -1.16,-0.65 -1.25,-1.31 z"></path>

      <path class="sgc-1" id="path20" d="m 193.53,669.51 0,0.22 -0.01,0.23 0,0.23 -0.01,0.24 -0.02,0.51 -0.04,0.52 -0.05,0.55 -0.06,0.57 -0.08,0.58 -0.1,0.6 -0.12,0.61 -0.14,0.62 -0.16,0.62 -0.18,0.64 -0.21,0.63 -0.23,0.64 -0.13,0.32 -0.14,0.32 -0.14,0.31 -0.15,0.32 c -1.78,3.66 -4.34,5.59 -4.64,5.59 -0.18,0 -0.3,-0.12 -0.3,-0.3 0,-0.08 0,-0.15 0.57,-0.68 2.91,-2.95 4.61,-7.68 4.61,-13.89 0,-5.09 -1.1,-10.33 -4.79,-14.08 -0.39,-0.35 -0.39,-0.41 -0.39,-0.5 0,-0.18 0.12,-0.3 0.3,-0.3 0.3,0 2.98,2.02 4.73,5.8 1.52,3.27 1.88,6.58 1.88,9.08 z"></path>
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  </svg>

  <p>は &#402; の x = a における n 次導関数、&#402; の 0 次導関数は &#402; 自身である。また、</p>

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    <metadata id="metadata24">image/svg+xml</metadata>

    <defs id="defs22"></defs>

    <desc id="desc5">(x-a)^0</desc>

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      <path class="sgc-1" id="path10" d="m 126.58,671.05 0.02,0.08 0.02,0.09 0.02,0.1 0.03,0.11 0.03,0.11 0.04,0.13 0.04,0.12 0.04,0.14 0.05,0.14 0.05,0.14 0.06,0.15 0.06,0.14 0.07,0.15 0.07,0.15 0.07,0.15 0.09,0.15 0.09,0.14 0.09,0.15 0.1,0.13 0.1,0.14 0.12,0.12 0.11,0.12 0.13,0.12 0.13,0.1 0.14,0.1 0.14,0.08 0.08,0.04 0.08,0.04 0.08,0.03 0.08,0.03 0.08,0.03 0.08,0.02 0.09,0.02 0.09,0.02 0.09,0.01 0.09,0.01 0.1,0.01 0.09,0 c 0.15,0 0.87,0 1.49,-0.38 -0.83,-0.15 -1.43,-0.9 -1.43,-1.61 0,-0.48 0.33,-1.04 1.13,-1.04 0.66,0 1.61,0.53 1.61,1.72 0,1.55 -1.75,1.97 -2.77,1.97 -1.72,0 -2.76,-1.58 -3.12,-2.26 -0.74,1.96 -2.35,2.26 -3.22,2.26 -3.09,0 -4.78,-3.84 -4.78,-4.58 0,-0.3 0.29,-0.3 0.36,-0.3 0.23,0 0.32,0.06 0.38,0.33 1.01,3.15 2.97,3.89 3.99,3.89 0.56,0 1.6,-0.26 1.6,-1.99 0,-0.92 -0.5,-2.91 -1.6,-7.08 -0.48,-1.84 -1.52,-3.09 -2.83,-3.09 -0.18,0 -0.86,0 -1.49,0.38 0.75,0.15 1.4,0.77 1.4,1.61 0,0.8 -0.65,1.04 -1.1,1.04 -0.89,0 -1.64,-0.77 -1.64,-1.73 0,-1.36 1.49,-1.96 2.8,-1.96 1.97,0 3.04,2.08 3.13,2.26 0.35,-1.1 1.42,-2.26 3.21,-2.26 3.06,0 4.76,3.84 4.76,4.58 0,0.3 -0.27,0.3 -0.36,0.3 -0.27,0 -0.33,-0.12 -0.39,-0.33 -0.98,-3.18 -3,-3.89 -3.96,-3.89 -1.15,0 -1.63,0.95 -1.63,1.96 0,0.66 0.18,1.31 0.51,2.62 z"></path>

      <path class="sgc-1" id="path12" d="m 159.86,668.91 0.1,0 0.09,0 0.1,0 0.04,0.01 0.05,0 0.05,0 0.04,0.01 0.04,0 0.05,0.01 0.04,0.01 0.04,0.01 0.04,0.01 0.04,0.01 0.03,0.02 0.04,0.02 0.03,0.01 0.03,0.03 0.03,0.02 0.03,0.02 0.02,0.03 0.02,0.03 0.02,0.02 0.01,0.01 0,0.02 0.01,0.02 0.01,0.02 0.01,0.02 0.01,0.02 0,0.02 0.01,0.02 0,0.02 0.01,0.03 0,0.02 0,0.02 0,0.03 0.01,0.03 0,0.02 c 0,0.6 -0.54,0.6 -1.05,0.6 h -16.09 c -0.5,0 -1.04,0 -1.04,-0.6 0,-0.59 0.54,-0.59 1.04,-0.59 z"></path>

      <path class="sgc-1" id="path14" d="m 181.1,673.31 -0.05,0.1 -0.06,0.11 -0.05,0.09 -0.06,0.1 -0.06,0.09 -0.06,0.1 -0.06,0.09 -0.07,0.08 -0.07,0.09 -0.06,0.08 -0.08,0.08 -0.07,0.08 -0.08,0.07 -0.08,0.08 -0.08,0.06 -0.08,0.07 -0.09,0.06 -0.08,0.06 -0.09,0.05 -0.1,0.06 -0.09,0.04 -0.1,0.05 -0.1,0.04 -0.1,0.04 -0.11,0.03 -0.1,0.03 -0.11,0.02 -0.12,0.02 -0.11,0.02 -0.12,0.01 -0.12,0.01 -0.13,0 c -3.48,0 -7.17,-4.38 -7.17,-8.72 0,-2.8 1.64,-4.76 3.96,-4.76 l 0.06,0.66 c -1.49,0 -1.91,1.63 -1.91,2.79 0,1.49 0.96,5.15 1.64,6.52 0.92,1.75 2.26,2.85 3.45,2.85 1.93,0 2.35,-2.44 2.35,-2.61 0,-0.18 -0.06,-0.36 -0.09,-0.51 l -1.49,-5.84 c -0.14,-0.53 -0.14,-0.59 -0.59,-1.09 -1.31,-1.64 -2.53,-2.11 -3.36,-2.11 l -0.06,-0.66 c 0.59,0 2.08,0.12 3.87,2.23 0.23,-1.25 1.28,-2.23 2.7,-2.23 1.05,0 1.73,0.69 2.21,1.64 0.5,1.07 0.89,2.88 0.89,2.94 0,0.3 -0.27,0.3 -0.36,0.3 -0.3,0 -0.33,-0.12 -0.42,-0.53 -0.5,-1.94 -1.04,-3.69 -2.26,-3.69 -0.8,0 -0.89,0.77 -0.89,1.37 0,0.65 0.06,0.89 0.39,2.2 0.32,1.25 0.38,1.54 0.65,2.68 l 1.07,4.16 c 0.21,0.83 0.21,0.89 0.21,1.01 0,0.5 -0.36,0.8 -0.86,0.8 -0.72,0 -1.16,-0.65 -1.25,-1.31 z"></path>

      <path class="sgc-1" id="path16" d="m 194.34,669.51 0,0.22 -0.01,0.23 0,0.23 -0.01,0.24 -0.03,0.51 -0.03,0.52 -0.05,0.55 -0.06,0.57 -0.08,0.58 -0.1,0.6 -0.12,0.61 -0.14,0.62 -0.16,0.62 -0.18,0.64 -0.21,0.63 -0.23,0.64 -0.13,0.32 -0.14,0.32 -0.14,0.31 -0.15,0.32 c -1.78,3.66 -4.34,5.59 -4.64,5.59 -0.18,0 -0.3,-0.12 -0.3,-0.3 0,-0.08 0,-0.15 0.57,-0.68 2.91,-2.95 4.61,-7.68 4.61,-13.89 0,-5.09 -1.1,-10.33 -4.79,-14.08 -0.39,-0.35 -0.39,-0.41 -0.39,-0.5 0,-0.18 0.12,-0.3 0.3,-0.3 0.3,0 2.98,2.02 4.73,5.8 1.52,3.27 1.88,6.58 1.88,9.08 z"></path>

      <path class="sgc-1" id="path18" d="m 208.07,679.49 -0.01,0.42 -0.01,0.41 -0.02,0.39 -0.02,0.39 -0.04,0.36 -0.04,0.36 -0.05,0.34 -0.07,0.34 -0.07,0.32 -0.09,0.32 -0.1,0.31 -0.11,0.3 -0.13,0.29 -0.14,0.29 -0.16,0.28 -0.08,0.14 -0.09,0.13 c -0.65,0.96 -1.94,1.8 -3.61,1.8 -4.82,0 -4.82,-5.69 -4.82,-7.19 0,-1.5 0,-7.06 4.82,-7.06 v 0.58 c -0.95,0 -2.22,0.56 -2.64,2.27 -0.29,1.23 -0.29,2.94 -0.29,4.48 0,1.52 0,3.1 0.31,4.25 0.44,1.64 1.77,2.08 2.62,2.08 1.13,0 2.21,-0.69 2.59,-1.89 0.33,-1.13 0.35,-2.63 0.35,-4.44 0,-1.54 0,-3.08 -0.27,-4.4 -0.42,-1.89 -1.83,-2.35 -2.67,-2.35 h 0 v -0.58 c 4.84,0 4.84,5.56 4.84,7.06 z"></path>
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  </svg>

  <p>と 0! は 1 と定義されている。この冪級数がもとの関数 f(x) に一致するとき、f(x) はテイラー展開可能であるという。</p>
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