MR2440940 Mitsuo KATO Mitsuo KATO Funkcialaj Ekvacioj. Serio Internacia 51 2008 221--243 http://fe.math.kobe-u.ac.jp/FE/FullPapers/51-2/51_221.pdf http://www.ams.org/mathscinet-getitem?mr=MR2440940 Let $E(x)$ be the third order differential equation ${}_3E_2$ satisfied by a generalized hypergeometric function ${}_3F_2(a_0,a_1,a_2;b_1,b_2;x)$. Under some assumptions which guarantee that $E(x)$ is irreducible and has no logarithmic solutions, we determine all the algebraic transformations $E(x)=\theta(x)E'(\varphi(x))$, where $E'(z)$ is a Fuchsian differential equation on ${\bf P}^1$, $\varphi(x)$ a rational function, and $\theta(x)$ a finite product of complex powers of rational functions. We find $E'(z)$ also turns out to be a ${}_3E_2$. Hypergeometric function, Fuchsian differential equation, Local exponent, Algebraic transformation. Primary 33C20. 51-221 2008 Mitsuo KATO Mitsuo KATO 1 Bailey, W. N. Generalized Hypergeometric Series Cambridge Tracts in Mathematics and Mathematical Physics 32 1935 MR0185155

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