We have the usual analogy between infinitesimal calculus (integrals and derivatives) and finite calculus (sums and forward differences), and also the generalization of infinitesimal calculus to fractional calculus (which allows for real and even complex powers of the differential operator). Have ...

Fractional derivative (differintegral) can be defined via Fourier or Laplace transform: ${\displaystyle D ^{q}f(t)={\mathcal {F}}^{-1}\left\{(i\omega )^{q}{\mathcal {F}}[f(t)]\right\}},$ ${\displaystyle D ^{q}f(t)={\mathcal {L}}^{-1}\left\{s^{q}{\mathcal {L}}[f(t)]\right\}.}$ This way, one can si...

Short answer: you don't want to consider group cohomology as defined for finite groups for Lie groups like $U(1)$, or indeed topological groups in general. There are other cohomology theories (not Stasheff's) that are the 'right' cohomology groups, in that there are the right isomorphisms in low ...

In answer to A coverage question Cam mentions an article by SOUND. I have been running a computer program for THIS and would like to know if there are a reasonable average and standard deviation for the class number, related to Dirichlet's formula for $d > 4$ $$ h(-d) = \sqrt d \; L(1, \chi_{-...