Graphical Representations of Depleted Zeta Subseries
Graphical Representations of Depleted Zeta Subseries
It is well-known that the harmonic series diverges; equivalently, equals infinity. Remarkably, modified forms of , denoted here by , can yield various converging values. For example, deleting all terms in the harmonic series whose denominator contains a 9 converges to approximately 23; this is known as the Kempner sum. More generally, represents a subseries of with terms deleted whose denominator's base representation contains the string of digits given by ….
ζ(1)
ζ
Ψ
Ψ(s,n,b)
ζ(s)
b
n
δ
1
δ
L