ESF - The Encyclopedia of Special Functions

About Equation AI.2.1.2.4

$\begin{equation*} \begin{split} u (3 n)& =\frac{3^{\bigl(\frac{1}{3} - 2 n\bigr)}}{3 \Gamma (n + 1) \Gamma \Bigl(n + \frac{2}{3}\Bigr)} \end{split} \end{equation*}$

$\begin{equation*} \begin{split} u (3 n + 1)& =\frac{-3^{\bigl(\frac{2}{3} - 2 n\bigr)}}{9 \Gamma (n + 1) \Gamma \Bigl(n + \frac{4}{3}\Bigr)} \end{split} \end{equation*}$

$\begin{equation*} \begin{split} u (3 n + 2)& =0 \end{split} \end{equation*}$

Absolute reference: AI:asympt:0:RDLBLRDGENFORMRDCLOSED

LaTeX encoding

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u (3 n) = \frac{3^{\bigl(\frac{1}{3} - 2 n\bigr)}}{3 \Gamma (n + 1) \Gamma \Bigl(n + \frac{2}{3}\Bigr)}

u (3 n + 1) = \frac{-3^{\bigl(\frac{2}{3} - 2 n\bigr)}}{9 \Gamma (n + 1) \Gamma \Bigl(n + \frac{4}{3}\Bigr)}

u (3 n + 2) = 0

Maple encoding

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u(3*n) = 1/3*3^(1/3-2*n)/GAMMA(n+1)/GAMMA(n+2/3)

u(3*n+1) = -1/9*3^(2/3-2*n)/GAMMA(n+1)/GAMMA(n+4/3)

u(3*n+2) = 0

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About Equation AI.2.1.2.4

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