07/29/2009, 03:41 PM
(This post was last modified: 07/29/2009, 03:52 PM by Kouznetsov.)

I did not found where to put these pics, to, I open this tread for plots of square root of factorial (left) and that of exponential (right).

\( f=\sqrt{!}(z) \) and \( f=\sqrt{\exp}(z) \) are shown with lines

\( p=\Re(f)=const \) and

\( q=\Im(f)=const \).

Levels \( p=-4, -3, -2, -1, 0, 1, 2 3,4 \) are shown with thick black lines.

Some intermediate Levels \( p= \)const

are shown with red lines of the nefative values and blue for the positive values.

Levels \( q=-4, -3, -2, -1 \) are shown with thick red lines.

Level \( q=0 \) is shown with dark pink.

Levels \( q=1,2,3,4 \) are shown with thick blue lines.

Some intermediate levels \( q= \)const are shown with green.

Cuts are shown with black dashed lines.

Such functions are solutions of the equations

\( \sqrt{!~}\Big( \sqrt{!~} \big(z\big) \Big)=z! \) and

\( \sqrt{\exp}\Big( \sqrt{\exp} \big(z\big) \Big)=\exp(z) \)

\( f=\sqrt{!}(z) \) and \( f=\sqrt{\exp}(z) \) are shown with lines

\( p=\Re(f)=const \) and

\( q=\Im(f)=const \).

Levels \( p=-4, -3, -2, -1, 0, 1, 2 3,4 \) are shown with thick black lines.

Some intermediate Levels \( p= \)const

are shown with red lines of the nefative values and blue for the positive values.

Levels \( q=-4, -3, -2, -1 \) are shown with thick red lines.

Level \( q=0 \) is shown with dark pink.

Levels \( q=1,2,3,4 \) are shown with thick blue lines.

Some intermediate levels \( q= \)const are shown with green.

Cuts are shown with black dashed lines.

Such functions are solutions of the equations

\( \sqrt{!~}\Big( \sqrt{!~} \big(z\big) \Big)=z! \) and

\( \sqrt{\exp}\Big( \sqrt{\exp} \big(z\big) \Big)=\exp(z) \)