Half-exponential function (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Half-exponential function" in English language version.

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5doi.org

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5ams.org

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1uni-goettingen.de

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ams.org

mathscinet.ams.org

Kneser, H. (1950). "Reelle analytische Lösungen der Gleichung $φ (φ (x) = e x$ und verwandter Funktionalgleichungen". Journal für die reine und angewandte Mathematik. 187: 56–67. doi:10.1515/crll.1950.187.56. MR 0035385.
Miltersen, Peter Bro; Vinodchandran, N. V.; Watanabe, Osamu (1999). "Super-polynomial versus half-exponential circuit size in the exponential hierarchy". In Asano, Takao; Imai, Hiroshi; Lee, D. T.; Nakano, Shin-ichi; Tokuyama, Takeshi (eds.). Computing and Combinatorics, 5th Annual International Conference, COCOON '99, Tokyo, Japan, July 26–28, 1999, Proceedings. Lecture Notes in Computer Science. Vol. 1627. Springer. pp. 210–220. doi:10.1007/3-540-48686-0_21. ISBN 978-3-540-66200-6. MR 1730337.
van der Hoeven, J. (2006). Transseries and Real Differential Algebra. Lecture Notes in Mathematics. Vol. 1888. Springer-Verlag, Berlin. doi:10.1007/3-540-35590-1. ISBN 978-3-540-35590-8. MR 2262194. 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. (1988). "Functional powers near a fixed point". Journal of Mathematical Analysis and Applications. 132 (2): 520–529. doi:10.1016/0022-247X(88)90080-7. MR 0943525.
Razborov, Alexander A.; Rudich, Steven (1997). "Natural proofs". Journal of Computer and System Sciences. 55 (1): 24–35. doi:10.1006/jcss.1997.1494. MR 1473047.

doi.org

Kneser, H. (1950). "Reelle analytische Lösungen der Gleichung $φ (φ (x) = e x$ und verwandter Funktionalgleichungen". Journal für die reine und angewandte Mathematik. 187: 56–67. doi:10.1515/crll.1950.187.56. MR 0035385.
Miltersen, Peter Bro; Vinodchandran, N. V.; Watanabe, Osamu (1999). "Super-polynomial versus half-exponential circuit size in the exponential hierarchy". In Asano, Takao; Imai, Hiroshi; Lee, D. T.; Nakano, Shin-ichi; Tokuyama, Takeshi (eds.). Computing and Combinatorics, 5th Annual International Conference, COCOON '99, Tokyo, Japan, July 26–28, 1999, Proceedings. Lecture Notes in Computer Science. Vol. 1627. Springer. pp. 210–220. doi:10.1007/3-540-48686-0_21. ISBN 978-3-540-66200-6. MR 1730337.
van der Hoeven, J. (2006). Transseries and Real Differential Algebra. Lecture Notes in Mathematics. Vol. 1888. Springer-Verlag, Berlin. doi:10.1007/3-540-35590-1. ISBN 978-3-540-35590-8. MR 2262194. 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. (1988). "Functional powers near a fixed point". Journal of Mathematical Analysis and Applications. 132 (2): 520–529. doi:10.1016/0022-247X(88)90080-7. MR 0943525.
Razborov, Alexander A.; Rudich, Steven (1997). "Natural proofs". Journal of Computer and System Sciences. 55 (1): 24–35. doi:10.1006/jcss.1997.1494. MR 1473047.

uni-goettingen.de

gdz.sub.uni-goettingen.de

Kneser, H. (1950). "Reelle analytische Lösungen der Gleichung $φ (φ (x) = e x$ und verwandter Funktionalgleichungen". Journal für die reine und angewandte Mathematik. 187: 56–67. doi:10.1515/crll.1950.187.56. MR 0035385.