About Equation AI.2.1.1.1 |
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![\begin{equation*}
\begin{split}
\operatorname{Ai} (x)& =\frac{\sqrt[3]{3}}{3 \Gamma \Bigl(\frac{2}{3}\Bigr)} - \frac{\sqrt[6]{3} \Gamma \Bigl(\frac{2}{3}\Bigr)}{2 \pi} x + \frac{\sqrt[3]{3}}{18 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{3} - \frac{\sqrt[6]{3} \Gamma \Bigl(\frac{2}{3}\Bigr)}{24 \pi} x^{4} + \\
& \quad{}\quad{}\frac{\sqrt[3]{3}}{540 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{6} - \frac{\sqrt[6]{3} \Gamma \Bigl(\frac{2}{3}\Bigr)}{1008 \pi} x^{7} + \frac{\sqrt[3]{3}}{38880 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{9} - \frac{\sqrt[6]{3} \Gamma \Bigl(\frac{2}{3}\Bigr)}{90720 \pi} \\
& \quad{}\quad{}x^{10} + \frac{\sqrt[3]{3}}{5132160 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{12} - \frac{\sqrt[6]{3} \Gamma \Bigl(\frac{2}{3}\Bigr)}{14152320 \pi} x^{13} + \frac{\sqrt[3]{3}}{1077753600 \Gamma \Bigl(\frac{2}{3}\Bigr)} \\
& \quad{}\quad{}x^{15} + \operatorname{O} \bigl(x^{16}\bigr)
\end{split}
\end{equation*}](NDIBAIIBSBGBIBasymptIBSBGB0SBGB_LBL_TERMS_EQPD_1.gif)
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LaTeX encoding |
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\operatorname{Ai} (x) = \frac{\sqrt[3]{3}}{3 \Gamma \Bigl(\frac{2}{3}\Bigr)} - \frac{\sqrt[6]{3} \Gamma \Bigl(\frac{2}{3}\Bigr)}{2 \pi} x + \frac{\sqrt[3]{3}}{18 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{3} - \frac{\sqrt[6]{3} \Gamma \Bigl(\frac{2}{3}\Bigr)}{24 \pi} x^{4} + \\
\quad{}\quad{}\frac{\sqrt[3]{3}}{540 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{6} - \frac{\sqrt[6]{3} \Gamma \Bigl(\frac{2}{3}\Bigr)}{1008 \pi} x^{7} + \frac{\sqrt[3]{3}}{38880 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{9} - \frac{\sqrt[6]{3} \Gamma \Bigl(\frac{2}{3}\Bigr)}{90720 \pi} \\
\quad{}\quad{}x^{10} + \frac{\sqrt[3]{3}}{5132160 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{12} - \frac{\sqrt[6]{3} \Gamma \Bigl(\frac{2}{3}\Bigr)}{14152320 \pi} x^{13} + \frac{\sqrt[3]{3}}{1077753600 \Gamma \Bigl(\frac{2}{3}\Bigr)} \\
\quad{}\quad{}x^{15} + \operatorname{O} \bigl(x^{16}\bigr)
Maple encoding |
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`&operatorname`(Ai)(x) = series(1/3*3^(1/3)/GAMMA(2/3)+(-1/2*3^(1/6)/Pi*GAMMA(2/3))*x+1/18*3^(1/3)/GAMMA(2/3)*x^3+(-1/24*3^(1/6)/Pi*GAMMA(2/3))*x^4+1/540*3^(1/3)/GAMMA(2/3)*x^6+(-1/1008*3^(1/6)/Pi*GAMMA(2/3))*x^7+1/38880*3^(1/3)/GAMMA(2/3)*x^9+(-1/90720*3^(1/6)/Pi*GAMMA(2/3))*x^10+1/5132160*3^(1/3)/GAMMA(2/3)*x^12+(-1/14152320*3^(1/6)/Pi*GAMMA(2/3))*x^13+1/1077753600*3^(1/3)/GAMMA(2/3)*x^15+O(x^16),x,16)