半指數函數 (Chinese Wikipedia)

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Kneser, H. Reelle analytische Lösungen der Gleichung $φ (φ (x) = e x$ und verwandter Funktionalgleichungen. Journal für die reine und angewandte Mathematik. 1950, 187: 56–67 [2022-06-22]. MR 0035385. （原始内容存档于2022-05-18）.
Miltersen, Peter Bro; Vinodchandran, N. V.; Watanabe, Osamu. Asano, Takao; Imai, Hiroshi; Lee, D. T.; Nakano, Shin{-}Ichi; Tokuyama, Takeshi , 编. Computing and Combinatorics, 5th Annual International Conference, COCOON '99, Tokyo, Japan, July 26-28, 1999, Proceedings. Lecture Notes in Computer Science 1627. Springer: 210–220. 1999. MR 1730337. doi:10.1007/3-540-48686-0_21. |contribution=被忽略 (帮助)
van der Hoeven, J. Transseries and real differential algebra. Lecture Notes in Mathematics 1888. Springer-Verlag, Berlin. 2006. ISBN 978-3-540-35590-8. MR 2262194. doi:10.1007/3-540-35590-1. . See exercise 4.10, p. 91, according to which every such function has a comparable growth rate to an exponential or logarithmic function iterated an integer number of times, rather than the half-integer that would be required for a half-exponential function.
Crone, Lawrence J.; Neuendorffer, Arthur C. Functional powers near a fixed point. Journal of Mathematical Analysis and Applications. 1988, 132 (2): 520–529. MR 0943525. doi:10.1016/0022-247X(88)90080-7 .
Razborov, Alexander A.; Rudich, Steven. Natural proofs. Journal of Computer and System Sciences. 1997, 55 (1): 24–35. MR 1473047. doi:10.1006/jcss.1997.1494 .

Miltersen, Peter Bro; Vinodchandran, N. V.; Watanabe, Osamu. Asano, Takao; Imai, Hiroshi; Lee, D. T.; Nakano, Shin{-}Ichi; Tokuyama, Takeshi , 编. Computing and Combinatorics, 5th Annual International Conference, COCOON '99, Tokyo, Japan, July 26-28, 1999, Proceedings. Lecture Notes in Computer Science 1627. Springer: 210–220. 1999. MR 1730337. doi:10.1007/3-540-48686-0_21. |contribution=被忽略 (帮助)
van der Hoeven, J. Transseries and real differential algebra. Lecture Notes in Mathematics 1888. Springer-Verlag, Berlin. 2006. ISBN 978-3-540-35590-8. MR 2262194. doi:10.1007/3-540-35590-1. . See exercise 4.10, p. 91, according to which every such function has a comparable growth rate to an exponential or logarithmic function iterated an integer number of times, rather than the half-integer that would be required for a half-exponential function.
Crone, Lawrence J.; Neuendorffer, Arthur C. Functional powers near a fixed point. Journal of Mathematical Analysis and Applications. 1988, 132 (2): 520–529. MR 0943525. doi:10.1016/0022-247X(88)90080-7 .
Razborov, Alexander A.; Rudich, Steven. Natural proofs. Journal of Computer and System Sciences. 1997, 55 (1): 24–35. MR 1473047. doi:10.1006/jcss.1997.1494 .