\u30bc\u30fc\u30bf\u95a2\u6570\u306e\u3046\u3061\u3001$\\zeta(2)$\u306f<\/p>\n
\\begin{align}
\n\\zeta(2) &= \\sum_{n=1}^{\\infty}\\frac{1}{n^2} \\nonumber\\cr
\n&= \\frac{\\pi^2}{6} \\label{eq:basel}
\n\\end{align}<\/p>\n
\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n
\u3053\u306e\u7d50\u679c\u3092\u4f7f\u3063\u3066$\\zeta(4)$\u306e\u8a08\u7b97\u304c\u3067\u304d\u306a\u3044\u304b\u8003\u3048\u3066\u307f\u308b\u3053\u3068\u306b\u3057\u307e\u3057\u305f\u3002<\/p>\n
\u6700\u521d\u306b$\\zeta(2)$\u3092\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3092\u4f7f\u3063\u3066\u6c42\u3081\u307e\u3059\u3002<\/p>\n
\u3068\u308a\u3042\u3048\u305a\u3001(\\ref{eq:fonex})\u5f0f\u306e\u95a2\u6570\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n
\\begin{align}
\nf_1(x)&= x^2 (x \\in \\left[ -\\pi, \\pi \\right])\\label{eq:fonex}
\n\\end{align}<\/p>\n
(\\ref{eq:fonex})\u5f0f\u3092\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3059\u308b\u3068\u3001(\\ref{eq:fonex})\u5f0f\u306f\u5076\u95a2\u6570\u3067\u3042\u308b\u3053\u3068\u304b\u3089\u3001<\/p>\n
\\begin{align}
\nf_1(x) &= \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} a_n\\cos nx\\label{eq:fonefourier}
\n\\end{align}<\/p>\n
\u305f\u3060\u3057\u3001<\/p>\n
\\begin{align}
\na_n &= \\frac{1}{\\pi}\\int_{-\\pi}^{\\pi}f_1(t)\\cos nt\\, dt \\nonumber \\cr
\n&= \\frac{1}{\\pi}\\int_{-\\pi}^{\\pi}t^2\\cos nt\\, dt \\label{eq:fonecoefficient}
\n\\end{align}<\/p>\n
\u3068\u306a\u308a\u307e\u3059\u306e\u3067\u3001(\\ref{eq:fonecoefficient})\u5f0f\u306e\u53f3\u8fba\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n
$n \\gt 0$\u306e\u5834\u5408\u306f\u3001(\\ref{eq:fonecoefficient})\u5f0f\u306e\u53f3\u8fba\u306f\u90e8\u5206\u7a4d\u5206\u3092\u4f7f\u3063\u3066\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n
\u3059\u308b\u3068\u2026<\/p>\n
\\begin{align}
\na_n &= \\frac{1}{\\pi}\\int_{-\\pi}^{\\pi}t^2\\left(\\frac{1}{n}\\sin nt\\right)^{\\prime}\\, dt \\nonumber\\cr
\n&= \\frac{1}{n\\pi}\\left(\\left[t^2\\sin nt\\right]_{-\\pi}^{\\pi}-\\int_{-\\pi}^{\\pi}2t\\sin nt\\, dt\\right) \\nonumber\\cr
\n&= \\frac{1}{n\\pi}\\left(-\\int_{-\\pi}^{\\pi}2t\\sin nt\\, dt\\right)\\nonumber\\cr
\n&= \\frac{1}{n\\pi}\\int_{-\\pi}^{\\pi}2t\\left(\\frac{1}{n}\\cos nt\\right)^{\\prime}\\, dt\\nonumber\\cr
\n&= \\frac{2}{n^2\\pi}\\left(\\left[t\\cos nt\\right]_{-\\pi}^{\\pi}-\\int_{-\\pi}^{\\pi}\\cos nt\\, dt\\right)\\nonumber\\cr
\n&= \\frac{2}{n^2\\pi}\\left((-1)^n\\pi-(-1)^n(-\\pi)-\\left[\\frac{1}{n}\\sin nt\\right]_{-\\pi}^{\\pi}\\right)\\label{eq:fonecoefficientsecond}\\cr
\n&= (-1)^n\\frac{4}{n^2}\\label{eq:fonecoefficientthird}
\n\\end{align}<\/p>\n
\u3068\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u306a\u304a\u3001(\\ref{eq:fonecoefficientsecond})\u5f0f\u306e\u8a08\u7b97\u306b\u306f$n$\u304c\u6574\u6570\u306e\u6642\u306b$\\cos nx=(-1)^n$\u306b\u306a\u308b\u3053\u3068\u3092\u3001(\\ref{eq:fonecoefficientthird})\u5f0f\u306e\u8a08\u7b97\u306b\u306f$n$\u304c\u6574\u6570\u306e\u6642\u306b$\\sin nx=0$\u306b\u306a\u308b\u3053\u3068\u3092\u305d\u308c\u305e\u308c\u5229\u7528\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n
$n = 0$\u306e\u5834\u5408\u306f(\\ref{eq:fonecoefficient})\u5f0f\u306f\u3001<\/p>\n
\\begin{align}
\na_0 &= \\dfrac{1}{\\pi}\\int_{-\\pi}^{\\pi}f(t)dt \\nonumber \\cr
\n&= \\dfrac{1}{\\pi}\\int_{-\\pi}^{\\pi}t^2\\,dt\\nonumber\\cr
\n&= \\dfrac{1}{\\pi}\\left[\\displaystyle\\frac{t^3}{3}\\right]_{-\\pi}^{\\pi}\\nonumber\\cr
\n&= \\frac{2\\pi^2}{3}\\label{eq:fonecoefficientatzero}
\n\\end{align}<\/p>\n
\u3068\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n
(\\ref{eq:fonecoefficientthird})\u5f0f\u53ca\u3073(\\ref{eq:fonecoefficientatzero})\u5f0f\u3092(\\ref{eq:fonefourier})\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068\u2026
\n\\begin{align}
\nf_1(x) &= \\frac{\\pi^2}{3} + \\sum_{n=1}^{\\infty}(-1)^n\\frac{4}{n^2}\\cos nx \\label{eq:fonefourierfinal}
\n\\end{align}
\n\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n
\u3053\u3053\u3067\u3001(\\ref{eq:fonefourierfinal})\u5f0f\u306b$x=\\pi$\u3092\u4ee3\u5165\u3059\u308b\u3068\u3001$\\cos nx = (-1)^n$\u306b\u306a\u308a\u307e\u3059\u306e\u3067\u3001
\n\\begin{align}
\nf_1(\\pi) &= \\frac{\\pi^2}{3} + \\sum_{n=1}^{\\infty}(-1)^n\\frac{4}{n^2}(-1)^n\\nonumber\\cr
\n&= \\frac{\\pi^2}{3} + \\sum_{n=1}^{\\infty}\\frac{4}{n^2}\\label{eq:squareofpi}
\n\\end{align}
\n\u3068\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n
(\\ref{eq:squareofpi})\u5f0f\u306e\u53f3\u8fba\u306f$\\pi^2$\u306b\u7b49\u3057\u3044\u306e\u3067\u2026<\/p>\n
\\begin{align}
\n\\sum_{n=1}^{\\infty}\\frac{4}{n^2} &= \\dfrac{2\\pi^2}{3} \\label{eq:baselsecond}
\n\\end{align}<\/p>\n
\u3068\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n
\u3088\u3063\u3066\u3001(\\ref{eq:baselsecond})\u5f0f\u306e\u4e21\u8fba\u30924\u3067\u5272\u308b\u3068\u3001<\/p>\n
\\begin{align}
\n\\sum_{n=1}^{\\infty}\\frac{1}{n^2} &= \\dfrac{\\pi^2}{6} \\label{eq:baselfinal}
\n\\end{align}
\n\u3068\u306a\u308b\u3053\u3068\u304c\u793a\u305b\u307e\u3059\u3002$\\blacksquare$<\/p>\n
$\\zeta(2)$\u306e\u8a08\u7b97\u304c\u3067\u304d\u305f\u3068\u3053\u308d\u3067\u3001\u3053\u306e\u8a18\u4e8b\u306e\u672c\u984c\u3067\u3042\u308b$\\zeta(4)$\u306e\u8a08\u7b97\u306b\u79fb\u308a\u307e\u3059\u3002<\/p>\n
\u307e\u305a\u3001(\\ref{eq:ftwox})\u5f0f\u306e\u95a2\u6570\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n
\\begin{align}
\nf_2(x)&= x^4 (x \\in \\left[ -\\pi, \\pi \\right])\\label{eq:ftwox}
\n\\end{align}
\n(\\ref{eq:ftwox})\u5f0f\u3092\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3059\u308b\u3068\u3001(\\ref{eq:ftwox})\u5f0f\u306f\u5076\u95a2\u6570\u3067\u3042\u308b\u3053\u3068\u304b\u3089\u3001<\/p>\n
\\begin{align}
\nf_2(x) &= \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} a_n\\cos nx\\label{eq:ftwofourier}
\n\\end{align}<\/p>\n
\u305f\u3060\u3057\u3001<\/p>\n
\\begin{align}
\na_n &= \\frac{1}{\\pi}\\int_{-\\pi}^{\\pi}f(t)\\cos nt\\, dt \\nonumber \\cr
\n&= \\frac{1}{\\pi}\\int_{-\\pi}^{\\pi}t^4\\cos nt\\, dt \\label{eq:ftwocoefficient}
\n\\end{align}<\/p>\n
\u3068\u306a\u308a\u307e\u3059\u306e\u3067\u3001(\\ref{eq:ftwocoefficient})\u5f0f\u306e\u53f3\u8fba\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n
$\\zeta(2)$\u306e\u5834\u5408\u3068\u540c\u69d8\u306b\u3001$n \\gt 0$\u306e\u5834\u5408\u306f\u3001(\\ref{eq:ftwocoefficient})\u5f0f\u306e\u53f3\u8fba\u306f\u90e8\u5206\u7a4d\u5206\u3092\u4f7f\u3063\u3066\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n
(\\ref{eq:ftwocoefficient})\u5f0f\u306e\u7a4d\u5206\u306e\u88ab\u7a4d\u5206\u95a2\u6570\u306b$t^4$\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u306e\u3067\u8a08\u7b97\u91cf\u304c\u591a\u304f\u306a\u308a\u305d\u3046\u3067\u3059\u304c\u3001\u9811\u5f35\u3063\u3066\u8a08\u7b97\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n
\u3059\u308b\u3068\u2026<\/p>\n
\\begin{align}
\na_n &= \\frac{1}{\\pi}\\int_{-\\pi}^{\\pi}t^4\\left(\\frac{1}{n}\\sin nt\\right)^{\\prime}\\, dt \\nonumber\\cr
\n&= \\frac{1}{n\\pi}\\left(\\left[t^4\\sin nt\\right]_{-\\pi}^{\\pi}-\\int_{-\\pi}^{\\pi}4t^3\\sin nt\\, dt\\right) \\nonumber\\cr
\n&= \\frac{1}{n\\pi}\\left(-\\int_{-\\pi}^{\\pi}4t^3\\sin nt\\, dt\\right)\\nonumber\\cr
\n&= \\frac{1}{n\\pi}\\int_{-\\pi}^{\\pi}4t^3\\left(\\frac{1}{n}\\cos nt\\right)^{\\prime}\\, dt\\nonumber\\cr
\n&= \\frac{1}{n^2\\pi}\\left(\\left[4t^3\\cos nt\\right]_{-\\pi}^{\\pi}-\\int_{-\\pi}^{\\pi}12t^2\\cos nt\\, dt\\right)\\nonumber\\cr
\n&= \\frac{1}{n^2\\pi}\\left(\\left[4t^3\\cos nt\\right]_{-\\pi}^{\\pi}-12\\int_{-\\pi}^{\\pi}t^2\\cos nt\\, dt\\right)\\label{eq:ftwocoefficientsecond}
\n\\end{align}<\/p>\n
\u3053\u3053\u3067\u3001(\\ref{eq:fonecoefficient})\u5f0f\u53ca\u3073(\\ref{eq:fonecoefficientthird})\u5f0f\u3088\u308a\u3001
\n\\begin{align}
\n\\int_{-\\pi}^{\\pi}t^2\\cos nt\\, dt &= (-1)^n\\frac{4\\pi}{n^2} \\label{eq:ftwocoefficientthird}
\n\\end{align}
\n\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u306e\u3067\u3001(\\ref{eq:ftwocoefficientthird})\u5f0f\u3092(\\ref{eq:ftwocoefficientsecond})\u5f0f\u306b\u4ee3\u5165\u3057\u3066\u2026<\/p>\n
\\begin{align}
\n\\frac{1}{n^2\\pi}\\left(\\left[4t^3\\cos nt\\right]_{-\\pi}^{\\pi}-12\\int_{-\\pi}^{\\pi}t^2\\cos nt\\, dt\\right) &= \\frac{1}{n^2\\pi}\\left( 8\\pi^3(-1)^n – 12 (-1)^n\\frac{4\\pi}{n^2}\\right)\\nonumber\\cr
\n&= \\frac{1}{n^2\\pi}\\left( 8\\pi^3(-1)^n – 48 (-1)^n\\frac{\\pi}{n^2}\\right)\\nonumber\\cr
\n&= \\frac{(-1)^n}{n^2}\\left( 8\\pi^2 – \\frac{48}{n^2}\\right)\\label{eq:ftwocoefficientfourth}
\n\\end{align}
\n\u3068\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n
$n = 0$\u306e\u5834\u5408\u306f(\\ref{eq:ftwocoefficient})\u5f0f\u306f\u3001<\/p>\n
\\begin{align}
\na_0 &= \\dfrac{1}{\\pi}\\int_{-\\pi}^{\\pi}f(t)dt \\nonumber \\cr
\n&= \\dfrac{1}{\\pi}\\int_{-\\pi}^{\\pi}t^4\\,dt\\nonumber\\cr
\n&= \\dfrac{1}{\\pi}\\left[\\displaystyle\\frac{t^5}{5}\\right]_{-\\pi}^{\\pi}\\nonumber\\cr
\n&= \\frac{2\\pi^4}{5}\\label{eq:ftwocoefficientatzero}
\n\\end{align}<\/p>\n
\u3068\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n
(\\ref{eq:ftwocoefficientfourth})\u5f0f\u53ca\u3073(\\ref{eq:ftwocoefficientatzero})\u5f0f\u3092(\\ref{eq:ftwofourier})\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001$f_2(x)$\u306f
\n\\begin{align}
\nf_2(x) &= \\frac{\\pi^4}{5} + \\sum_{n=1}^{\\infty}\\frac{(-1)^n}{n^2}\\left( 8\\pi^2 – \\frac{48}{n^2}\\right) \\cos nx \\label{eq:ftwofourierfinal}
\n\\end{align}
\n\u3068\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\u3067\u304d\u307e\u3059\u3002<\/p>\n
(\\ref{eq:ftwofourierfinal})\u5f0f\u3067$x = \\pi$\u3068\u3059\u308b\u3068\u3001$\\cos n\\pi = (-1)^n$\u3067\u3059\u306e\u3067\u2026
\n\\begin{align}
\nf_2(\\pi) &= \\frac{\\pi^4}{5} + \\sum_{n=1}^{\\infty}\\frac{(-1)^n}{n^2}\\left( 8\\pi^2 – \\frac{48}{n^2}\\right) (-1)^n \\nonumber\\cr
\n&= \\frac{\\pi^4}{5} + \\sum_{n=1}^{\\infty}\\frac{1}{n^2}\\left( 8\\pi^2 – \\frac{48}{n^2}\\right) \\nonumber\\cr
\n&= \\frac{\\pi^4}{5} + \\sum_{n=1}^{\\infty}\\frac{1}{n^2}\\left( 8\\pi^2 – \\frac{48}{n^2}\\right)\\nonumber\\cr
\n&= \\frac{\\pi^4}{5} + \\sum_{n=1}^{\\infty}\\frac{8\\pi^2}{n^2} – \\sum_{n=1}^{\\infty}\\frac{48}{n^4}\\nonumber\\cr
\n&= \\frac{\\pi^4}{5} + 8\\pi^2\\sum_{n=1}^{\\infty}\\frac{1}{n^2} – \\sum_{n=1}^{\\infty}\\frac{48}{n^4}\\label{eq:ftwoatpi}
\n\\end{align}
\n\u3068\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n
(\\ref{eq:ftwoatpi})\u5f0f\u306e\u53f3\u8fba\u7b2c2\u9805\u306f(\\ref{eq:baselfinal})\u5f0f\u306e\u7d50\u679c\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u3001
\n\\begin{align}
\nf_2(\\pi) &= \\frac{\\pi^4}{5} + 8\\pi^2\\frac{\\pi^2}{6} – \\sum_{n=1}^{\\infty}\\frac{48}{n^4}\\nonumber\\cr
\n&= \\pi^4\\left(\\frac{1}{5} + \\frac{4}{3}\\right) – \\sum_{n=1}^{\\infty}\\frac{48}{n^4}\\nonumber\\cr
\n&= \\frac{23}{15}\\pi^4-\\sum_{n=1}^{\\infty}\\frac{48}{n^4} \\label{eq:equation}
\n\\end{align}
\n\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n
(\\ref{eq:equation})\u5f0f\u306e\u53f3\u8fba\u306f$\\pi^4$\u306b\u7b49\u3057\u3044\u3053\u3068\u304b\u3089\u2026
\n\\begin{align}
\n\\frac{8}{15}\\pi^4 &= \\sum_{n=1}^{\\infty}\\frac{48}{n^4} \\label{eq:equationsecond}
\n\\end{align}
\n\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u306e\u3067\u3001(\\ref{eq:equationsecond})\u5f0f\u306e\u4e21\u8fba\u309248\u3067\u5272\u308b\u3068\u2026
\n\\begin{align}
\n\\sum_{n=1}^{\\infty}\\frac{1}{n^4} &= \\frac{8}{15\\cdot48}\\pi^4 \\nonumber\\cr
\n&= \\frac{\\pi^4}{90} \\label{eq:zetaatfour}
\n\\end{align}
\n\u3068\u306a\u308a\u3001$\\zeta(4) = \\displaystyle\\frac{\\pi^4}{90}$\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002$\\blacksquare$<\/p>\n
$s$\u304c\u5076\u6570\u306e\u5834\u5408\u306e$\\zeta(s)$\u306b\u3064\u3044\u3066\u306f\u6f38\u5316\u5f0f\u304c\u3042\u308b\u3068Wikipedia\u306b\u66f8\u3044\u3066\u3042\u3063\u305f\u306e\u3067\u3001$\\zeta(2)$\u306e\u8a08\u7b97\u7d50\u679c\u3092\u4f7f\u3046\u3068$\\zeta(4)$\u306e\u8a08\u7b97\u304c\u3067\u304d\u308b\u306e\u3067\u306f\u306a\u3044\u304b\u3068\u8003\u3048\u305f\u306e\u3067\u3059\u304c\u3001\u306a\u3093\u3068\u304b\u8a08\u7b97\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n
\u307e\u305f\u3001$\\zeta(2)$\u306e\u8a08\u7b97\u306e\u9014\u4e2d\u3067\u5f97\u3089\u308c\u305f\u5f0f\u3092\u4f7f\u3046\u3053\u3068\u306b\u3088\u3063\u3066\u90e8\u5206\u7a4d\u5206\u306e\u8a08\u7b97\u3092\u4e00\u90e8\u7701\u7565\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u90e8\u5206\u7a4d\u5206\u306e\u8a08\u7b97\u306f\u9593\u9055\u3048\u3084\u3059\u3044\u4e0a\u306b\u8a08\u7b97\u91cf\u304c\u524a\u6e1b\u3067\u304d\u307e\u3059\u306e\u3067\u3001\u52a9\u304b\u308a\u307e\u3059\u306d\u3002<\/p>\n
\u3053\u306e\u8a18\u4e8b\u306f\u4ee5\u4e0a\u3067\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u306f\u3058\u3081\u306b \u30bc\u30fc\u30bf\u95a2\u6570\u306e\u3046\u3061\u3001$\\zeta(2)$\u306f \\begin{align} \\zeta(2) &= \\sum_{n=1}^{\\infty}\\frac{1}{n^2} \\nonumber\\cr &= \\frac{\\pi^2}{6} \\label{eq:basel} \\end{align} \u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u3053\u306e\u7d50\u679c\u3092\u4f7f\u3063\u3066$\\zeta(4)$\u306e\u8a08\u7b97\u304c\u3067\u304d\u306a\u3044\u304b\u8003\u3048\u3066\u307f\u308b\u2026 Read More »<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":9777,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":["post-9778","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-13"],"_links":{"self":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts\/9778","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9778"}],"version-history":[{"count":22,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts\/9778\/revisions"}],"predecessor-version":[{"id":9848,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts\/9778\/revisions\/9848"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/media\/9777"}],"wp:attachment":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9778"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9778"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9778"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}