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formal power series; superposition; boundary convergence

References:

[1] Bugajewski D., Gan X.-X.: **A note on formal power series**. Comment. Math. Univ. Carolin. 51 (2010), no. 4, 595–604. MR 2858263 | Zbl 1224.13025

[2] Bugajewski D., Gan X.-X.: **On formal Laurent series**. Bull. Braz. Math. Soc., New Series 42 (2011), no. 3, 415–437. DOI 10.1007/s00574-011-0023-6 | MR 2833811

[3] Gan X.-X., Knox N.: **On composition of formal power series**. Int. J. Math. Math. Sci. 30 (2002), no. 12, 761–770. DOI 10.1155/S0161171202107150 | MR 1917671 | Zbl 0998.13010

[4] Herzog F., Piranian, G.: **Sets of convergence of Taylor series I**. Duke Math. J. 16 (1949), 529–534. DOI 10.1215/S0012-7094-49-01647-6 | MR 0031049 | Zbl 0034.04806