Editing Weierstrass function (section)

==Hölder continuity==
It is convenient to write the Weierstrass function equivalently as

<math display="block">W_\alpha(x) = \sum_{n=0}^\infty b^{-n\alpha}\cos(b^n \pi x)</math>

for <math display="inline">\alpha = -\frac{\ln(a)}{\ln(b)}</math>.  Then <math display="inline">W_\alpha(x)</math> is [[Hölder continuous]] of exponent α, which is to say that there is a constant ''C'' such that

<math display="block">|W_\alpha(x)-W_\alpha(y)|\le C|x-y|^\alpha</math>

for all <math display="inline">x</math> and <math display="inline">y</math>.<ref>{{cite book | last1=Zygmund | first1=A. | title= Trigonometric Series |volume=I, II | title-link= Trigonometric Series | orig-year=1935 | publisher=[[Cambridge University Press]] | edition=3rd | series=Cambridge Mathematical Library | isbn=978-0-521-89053-3 | mr=1963498  | year=2002 |page=47}}</ref> Moreover, <math display="inline">W_1</math> is Hölder continuous of all orders <math display="inline">\alpha < 1</math> but not [[Lipschitz continuous]].