Szegö Curve

polynomial degree

20

show Szegö curve

The exponential function

x



has the Maclaurin series

x



=1+x+

1

2!

2

x

+

1

3!

3

x

+⋯+

1

n!

n

x

+⋯

. Truncating this series gives a polynomial of degree

n

. The roots of this polynomial in the complex plane, when scaled by

1

n

, approach the Szegö curve

z

1-z



=1

. Drag the slider to vary the polynomial degree

n

.