# Tag Archives: Confluent hypergeometric functions

## The Riemann Zeta and the Calculus

(Under construction: Reprising investigations over several years.) By virtue of the relation between the values of the Riemann zeta function at the negative integers, , and the Bernoulli numbers and between the Bernoulli polynomials and the partial sums of the … Continue reading

## 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 … Continue reading

## Goin’ with the Flow: Logarithm of the Derivative

Goin’ with the Flow: Logarithm of the Derivative Operator is a pdf set of notes under construction on the relations between the commutator of the logarithm of the derivative operator, the Pincherle derivative, Lie operator derivatives, and the two umbrally inverse … Continue reading

## A Generalized Dobinski Relation and the Confluent Hypergeometric Fcts.

The Inverse Mellin Transform, Bell Polynomials, a Generalized Dobinski Relation, and the Confluent Hypergeometric Functions presents a generalized Dobinski relation umbrally incorporating the Bell / Touchard / Exponential polynomials that is defined operationally through the action of the operator f(x d/dx) … Continue reading