Applied mathematics consulting.

RT @miniapeur:

What do distributions in analysis, things like Dirac deltas, have to do with distributions in probability?

Riemann zeta(4) = (π⁴)/90.

Riemann zeta(2) = (π²)/6.

Riemann zeta(0) = -1/2.

The Riemann zeta function is zero at all negative even integers.

Circular slide rules.

arctan( k tan(x) )

Hereafter, when they come to model heaven.And calculate the stars: how they will wield the.The mighty frame, how build, unbuild, contrive.To save appearances, how gird the sphere.With centric and eccentric scribbled o’er,.Cycle and epicycle, orb in orb. Milton, Paradise Lost

Harmonic functions are infinitely differentiable.

Thank you for following @AnalysisFact

Gamma function partial sums.

Newton's series looks typographically similar to Taylor's series.

If a function of a complex variable is differentiable once, it is infinitely differentiable (and analytic).

Orthogonal polynomials and Gaussian quadrature [pdf].

Paul Klee meets Perry the Platypus.

A non-constant analytic function maps open sets to open sets.

Harmonographs.

RT @TheMathFlow: The series 1/4+(1/4)²+(1/4)³+⋯=1/3.

If a function is analytic in a simply connected domain, it has a primitive (i.e. anti-derivative).