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stla committed Jul 25, 2022
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Expand Up @@ -94,7 +94,7 @@ For $n = 1$, the hypergeometric function of a matrix argument is known as the
It does not depend on $\alpha$. The case of $\sideset{\_2^{}}{\_1^{}}F$ is the most known,
this is the Gauss hypergeometric function. Let's check a value. It is known that

$$\sideset{\_2^{\thinspace}}{\_1^{}}F \left(\begin{matrix} 1/4, 1/2 \\\\ 3/4\end{matrix}; 80/81\right) = 1.8.$$
$$\sideset{\_{2\thinspace}^{}}{\_1^{}}F \left(\begin{matrix} 1/4, 1/2 \\\\ 3/4\end{matrix}; 80/81\right) = 1.8.$$

Since $80/81$ is close to $1$, the convergence is slow. We compute the truncated series below
for $m = 300$.
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