Geodesic
On linear independence of values of generalized polylogarithms
Sbornik. Mathematics, Tome 192 (2001) no. 8, pp. 1225-1239

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The linear independence of the values at certain rational points of generalized polylogarithms, which generate the algebra of all analytic functions with three logarithmic branch points, is established. Hermite–Padé approximations for an Angelesco–Nikishin system defined by a complete binary tree are used. 
@article{SM_2001_192_8_a6,
     author = {V. N. Sorokin},
     title = {On linear independence of values of generalized polylogarithms},
     journal = {Sbornik. Mathematics},
     pages = {1225--1239},
     publisher = {mathdoc},
     volume = {192},
     number = {8},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_8_a6/}
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V. N. Sorokin. On linear independence of values of generalized polylogarithms. Sbornik. Mathematics, Tome 192 (2001) no. 8, pp. 1225-1239. http://geodesic.mathdoc.fr/item/SM_2001_192_8_a6/