# Szegö Curve

Szegö Curve

The exponential function has the Maclaurin series . Truncating this series gives a polynomial of degree . The roots of this polynomial in the complex plane, when scaled by , approach the Szegö curve . Drag the slider to vary the polynomial degree .

x

=1+x+x+x+⋯+x+⋯

x

1

2 !

2

1

3 !

3

1

n !

n

n

1

n

|z|=1

1-z

n