# False Logarithm Series

False Logarithm Series

In a paper titled "Consideration of Some Series Which Are Distinguished by Special Properties", published in 1753, Leonhard Euler considers (x)=(1-x). He proves that ()=n for non-negative integers , just like ()=n, but shows that this function is different from (x). This Demonstration compares the plots of () and () for different values of . Red points correspond to pairs of integers on the line .

s

a

∞

∑

n=1

1

1-

n

a

n-1

∏

k=0

-k

a

s

a

n

a

n

log

a

n

a

log

a

s

a

x

a

log

a

x

a

a

y=x