ESF - The Encyclopedia of Special Functions

About Equation BI.2.1.1.1

$\begin{equation*} \begin{split} \operatorname{Bi} (x)& =\frac{3^{\frac{5}{6}}}{3 \Gamma \Bigl(\frac{2}{3}\Bigr)} + \frac{3^{\frac{2}{3}} \Gamma \Bigl(\frac{2}{3}\Bigr)}{2 \pi} x + \frac{3^{\frac{5}{6}}}{18 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{3} + \frac{3^{\frac{2}{3}} \Gamma \Bigl(\frac{2}{3}\Bigr)}{24 \pi} x^{4} + \\ & \quad{}\quad{}\frac{3^{\frac{5}{6}}}{540 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{6} + \frac{3^{\frac{2}{3}} \Gamma \Bigl(\frac{2}{3}\Bigr)}{1008 \pi} x^{7} + \frac{3^{\frac{5}{6}}}{38880 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{9} + \frac{3^{\frac{2}{3}} \Gamma \Bigl(\frac{2}{3}\Bigr)}{90720 \pi} \\ & \quad{}\quad{}x^{10} + \frac{3^{\frac{5}{6}}}{5132160 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{12} + \frac{3^{\frac{2}{3}} \Gamma \Bigl(\frac{2}{3}\Bigr)}{14152320 \pi} x^{13} + \frac{3^{\frac{5}{6}}}{1077753600 \Gamma \Bigl(\frac{2}{3}\Bigr)} \\ & \quad{}\quad{}x^{15} + \operatorname{O} \bigl(x^{16}\bigr) \end{split} \end{equation*}$

Absolute reference: BI:asympt:0:RDLBLRDTERMSRDEQ

LaTeX encoding

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\operatorname{Bi} (x) = \frac{3^{\frac{5}{6}}}{3 \Gamma \Bigl(\frac{2}{3}\Bigr)} + \frac{3^{\frac{2}{3}} \Gamma \Bigl(\frac{2}{3}\Bigr)}{2 \pi} x + \frac{3^{\frac{5}{6}}}{18 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{3} + \frac{3^{\frac{2}{3}} \Gamma \Bigl(\frac{2}{3}\Bigr)}{24 \pi} x^{4} + \\ \quad{}\quad{}\frac{3^{\frac{5}{6}}}{540 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{6} + \frac{3^{\frac{2}{3}} \Gamma \Bigl(\frac{2}{3}\Bigr)}{1008 \pi} x^{7} + \frac{3^{\frac{5}{6}}}{38880 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{9} + \frac{3^{\frac{2}{3}} \Gamma \Bigl(\frac{2}{3}\Bigr)}{90720 \pi} \\ \quad{}\quad{}x^{10} + \frac{3^{\frac{5}{6}}}{5132160 \Gamma \Bigl(\frac{2}{3}\Bigr)} x^{12} + \frac{3^{\frac{2}{3}} \Gamma \Bigl(\frac{2}{3}\Bigr)}{14152320 \pi} x^{13} + \frac{3^{\frac{5}{6}}}{1077753600 \Gamma \Bigl(\frac{2}{3}\Bigr)} \\ \quad{}\quad{}x^{15} + \operatorname{O} \bigl(x^{16}\bigr)

Maple encoding

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`&operatorname`(Bi)(x) = series(1/3*3^(5/6)/GAMMA(2/3)+1/2*3^(2/3)/Pi*GAMMA(2/3)*x+1/18*3^(5/6)/GAMMA(2/3)*x^3+1/24*3^(2/3)/Pi*GAMMA(2/3)*x^4+1/540*3^(5/6)/GAMMA(2/3)*x^6+1/1008*3^(2/3)/Pi*GAMMA(2/3)*x^7+1/38880*3^(5/6)/GAMMA(2/3)*x^9+1/90720*3^(2/3)/Pi*GAMMA(2/3)*x^10+1/5132160*3^(5/6)/GAMMA(2/3)*x^12+1/14152320*3^(2/3)/Pi*GAMMA(2/3)*x^13+1/1077753600*3^(5/6)/GAMMA(2/3)*x^15+O(x^16),x,16)