Geodesic
Algebraic independence of values of a~certain class of hypergeometric functions
Matematičeskie zametki, Tome 59 (1996) no. 3, pp. 402-414

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We prove a general theorem on the algebraic independence of values of hypergeometric $E$-functions and their successive derivatives at algebraic points for the “degenerate” case in which substantial cancellations occur in numerators and denominators of coefficients of the series in powers of $z$ of the functions considered. 
@article{MZM_1996_59_3_a8,
     author = {V. A. Kulagin},
     title = {Algebraic independence of values of a~certain class of hypergeometric functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {402--414},
     publisher = {mathdoc},
     volume = {59},
     number = {3},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_3_a8/}
}
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V. A. Kulagin. Algebraic independence of values of a~certain class of hypergeometric functions. Matematičeskie zametki, Tome 59 (1996) no. 3, pp. 402-414. http://geodesic.mathdoc.fr/item/MZM_1996_59_3_a8/