### Recent Comments

### Categories

### Meta

# Tag Archives: Digamma function

## Jumpin’ Riemann!…..!..!.!.Mangoldt–da mon–got it!….!..!

The magic of Mangoldt summoning Riemann’s miraculous miniscules-the nontrivial zeros. (Originally published in Sept. 2019. Inadvertanly deleted in April) In response to observations initiated by Matt McIrvin of a sum of exponentials of the imaginary part of the non-trivial zeroes … Continue reading

Posted in Math
Tagged Chebyshev function, Digamma function, Dirac delta function, Euler's product formula. Hadamard's product formula, Fourier transform, Inverse Mellin transform, Landau Xi function, logarithmic derivative, Mangoldt function, Mangoldt summatory function, Riemann jump function, Riemann Xi function, Riemann zeta function nontrivial zeros, Riemann's prime counting function
Leave a comment

## A Diorama of the Digamma

(Under construction) This series is divergent, so we may be able to do something with it. — Heaviside The divergent series for the pole of the Riemann zeta function is Lets’s use Mellin transform interpolation (essentially the master’s (Ramanujan) master … Continue reading

Posted in Math
Tagged Digamma function, Fractional calculus, gamma function, generalized harmonic numbers, harmonic numbers, infinigen, infinitesimal generator, Inverse Mellin transform, logarithmic derivative, Mellin integral transform, Mellin interpolation, Newton interpolation, power sum polynomials, reciprocal integers, Riemann zeta function, Rising factorial, Taylor series
Leave a comment

## 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