Weierstrass Function

In mathematics, the Weierstrass function was the first example found of a kind of function with the property that it is continuous everywhere but differentiable nowhere. Almost all continuous functions are nowhere differentiable, and this property is both stable and generic. Weierstrass functions are defined by f(x)=\sum_{n=0}^\infty a^n\cos(b^n\pi x), where 0 and
ab>1+\frac{3}{2}\pi.
The following graphs display the function f(x)=\sum_{n=0}^\infty (1/2)^n\cos(20^n\pi x), (Note: These graphs do not correctly display the function, they display only a subsampled version of this function.)

See also

 

<< PreviousWord BrowserNext >>
99 ranch market
canandaigua lake
bridge builder
alexandra ripley
heliconia
leyland cypress
alkimos
lee enfield no. 4
alstroemeria
joanna macgregor
jungle carbine
mps elected in the uk general election, 1979
uss sailfish
cryn fredericks
pointe shoes
svt 40
knowledge navigator
sit in
fort amsterdam
idaho transfer
norfolk island pine
basque music
uss nathanael greene (ssbn 636)
8:30
alexander hamilton u.s. custom house
dave weckl
leucoplast
bloody sunday (1887)
bloody sunday (1905)
songs of a circling spirit
stanley featherstonehaugh ukridge
international peace garden
due south
enterobacteria phage t2
coat of arms of yemen
elminster
ettin
gnoll
u.s. highway 281
butterbean
british committee for the restitution of the parthenon marbles
helmut jahn
muharram
come back, little sheba