The Creation / Raising Operators for Appell Sequences is a pdf presenting representations of the raising operator and its exponentiation for normal and logarithmic Appell sequences of polynomials as differential and integral operators. The Riemann zeta and digamma, or Psi, function are connected to fractional calculus and associated Appell sequences for a characteristic class discussed by Libgober and Lu.

## The Elliptic Lie Triad: KdV and Ricatti Equations, Infinigens, and Elliptic Genera

The Elliptic Lie Triad: Ricatti and KdV Equations, Infinigens, and Elliptic Genera

This site is not correctly updating, so the notes have been transcribed to this pdf.

## Snakes in the Appell Orchard

The Euler-Bernoulli numbers: what they count and associations to algebraic geometry, elliptic curves, and differential ops. Coming soon.

## Fractional Calculus, Gamma Classes, the Riemann Zeta Function, and an Appell Pair of Sequences

The background info and comments for the MSE question Lie group heuristics for a raising operator for and the MO question Riemann zeta function at positive integers and an Appell sequence of poylnomials introduce an Appell sequence of polynomials containing the Euler-Mascheroni constant and the Riemann zeta function evaluated at the integers greater than one. The Appell sequence can be defined by its e.g.f.

The raising op for the Appell sequence

where is the digamma or Psi function, is associated with the infinitesimal generator

of a class of fractional integro-derivatives through a change of variables (). Exponentiation gives

## A Class of Differential Operators and the Stirling Numbers

The differential operator with can easily be expanded in terms of the operators by considering its action on