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$B9)A!Bg$NDMK\(B$B$H?=$7$^$9(B.

$BMpF~$7$^$9(B.
The iterated power function x^x^x^... $B$r(B
$B:G=i$K8&5f$7$?$N$O(B ($BNc$K$h$C$F(B) Euler (1779),
$B$=$7$F(B Eisenstein (1844) $B$@$HJ*$NK\$K$"$j$^$9(B.
Euler $B$N$O%i%F%s8l(B, $BB>$NJ*$NK\$K$h$l$P(B,
Euler $B$ODj5A0h$,(B [e^{-e}, e^{1/e}] $B$G$"$k$3$H$r(B
$B<($7$?$=$&$G$9(B.
Eisenstein $B$N$O%I%$%D8l$G(B
"Entwicklung von $\alpha^{\alpha^{\alpha^{\cdot^{\cdot^\cdot}}}}$"
$B$H$$$&BjL>$NO@J8$G$9(B.
E(log z) = z^z^z^... $B$H$7$F(B$BDj5A$7$?(B E(z) $B$,(B
E(z) = \sum_{n=0}^\infty (n + 1)^{n-1} z^n/n!
$B$H$$$&E83+$r;}$D$3$H$,=q$$$F$"$k$N$G$O(B$B$J$$$+$H(B,
$B$3$l$OC1$J$kA[A|$G$9(B.
 ($BA4=8$rFI$s$G2?J}$+D4$Y$F2<$5$$$^$;$s$+(B.)
 ($B$I$A$i$b?'!9$J0UL#$G;d$K(B$B$OFI$a$^$;$s(B.)

x^x^x^... $B$K$D$$$F$N7k2L$O(B well-known $B$@$H;W$$$^$9$,(B,
$B!VJ?2lM=A[!W$OLLGr$$LdBj$@$H;W$$(B$B$^$9(B.

# $B2?8N$+(B Catalan $B?t$NOC$rD4$Y$F$$$F(B,
# $B>e$N$h$&$JNr;K$,=q$$$F$"$k$N$K5$IU$-$^$7$?(B.

# $B$3$N4X78(B$B$KIT?3$NG0$r;}$?$l$?J}$O(B
# Graham, Knuth, Patashnik "Concrete Mathematics"
# second edition $B$N(B 202 page $B$NA08e$r$4Mw2<$5$$(B.
--
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Tsukamoto, C. : chiaki@ipc.kit.ac.jp