The Fourier coefficients of x↦λxBn(x,y;λ) on [0,1) satisfy an arithmetical–dynamical transformation formula which makes the Fourier series amenable to a technique of generalized Möbius inversion. This yields some interesting arithmetic summation identities, among them parametrized versions of the following well-known classical formula of Davenport:
where μ(n) is the Möbius function and b809bb297b3833a5ae067d" title="Click to view the MathML source">{x} denotes the fractional part of x . Davenport's formula is the limiting case α=0 of which is valid for 90bed8722d3b" title="Click to view the MathML source">−π<α≤π.