### Recent Comments

### Categories

### Meta

# 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

Posted in Math
Tagged annihilation operator, Bernoulli numbers, Bernoulli polynomials, Beta integral, complex Cauchy contour integral, Confluent hypergeometric functions, convolution integral, creation operators, Differential operators, Digamma function, Dirac delta function, Fractional calculus, gamma function, Generalized Laguerre functions, generalized Laguerre polynomials, harmonic numbers, infinigen, infinitesimal generator, lowering operator, Mellin convolution, Mellin transform, operational calculus, Raising operators, Riemann zeta function, Sheffer Appell polynomials
Leave a comment

## 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

Posted in Math
Tagged Appell sequences, Associated Laguerre polynomials, Bell polynomials, Confluent hypergeometric functions, Convolution operators, Creation and annihilation operators, Cycle index polynomials, Differential operators, Digamma function, Falling factorials, Fractional calculus, Gamma classes, Gamma genus, Infinitesimal generators, Inverse Mellin transform, Mellin transform, Psi function, Raising and lowering operators, Riemann zeta function, Rising factorials, Umbral calculus, Umbral compositional inverse pair
Leave a comment

## 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

Posted in Math
Tagged Bell polynomials, Binomial Sheffer sequences, Commutatator, Confluent hypergeometric functions, Differential operators, Factorial polynomials, Falling factorial, Flow equations, Fractional calculus, Generalized Laguerre functions, Inversion, Laguerre polynomials, Lie derivatives, Logarithm of the derivative operator, Matrix representations, Operator calculus, Pincherle derivative, Rising factorial, Sheffer sequences, Simplices, Stirling numbers, Vandermonde matrix
1 Comment

## 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