x ( <0 ) |
-1 |
-2 |
-3 |
-4 |
-5 |
-6 |
-7 |
-8 |
-9 |
f(x)=x^x |
-1 |
1/4 |
-1/27 |
1/256 |
-1/3125 |
1/46656 |
-1/823543 |
1/16777216 |
-1/387420489 |
x=odd integer の時f(x)=-1 x=even integer の時 f(x)=1 |
x=無理数のときf(x)は存在しない |
x=有理数のとき | x=1/10,3/10,7/10,9/10の時 f(x)=(-1)^(1/10)=e^[i {(π/10)+(2nπ/10)}] =e^(±iπ/10), e^(±i 3π/10), e^(±i 7π/10), e^(±i 9π/10), |
x=1/3,5/3,1/4,3/4,5/4,7/4 1/5,3/5,7/5,9/5,1/6,5/6,7/6,11/6,1/7,3/7,5/7,9/7,11/7,13/7,1/8, 1/9,5/9,7/9,11/9,13/9,17/9,1/10,3/10,7/10,9/10,11/10,13/10,17/10,19/10, 1/11,3/11,5/11,7/11,9/11,13/11,15/11,17/11,19/11,21/11の時f(x)=-1 x=2/3,4/3, 2/5, 4/5,6/5,8/5,2/7,4/7,6/7,8/7,10/7,12/7,2/9,4/9,8/9, 10/9,14/9,16/9,2/11,4/11,6/11,8/11,10/11,12/11,14/11,16/11,18/11,20/11の時 f(x)=1 |
x=1/4, 3/4の時f(x)=±(1+i)/√2 |
x=1/2,3/2の時f(x)=±i |