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# Tag Archives: Inverse Mellin transform

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

The magic of Mangoldt summoning Riemann’s miraculous miniscules-the nontrivial zeros. In response to observations initiated by Matt McIrvin of a sum of exponentials of the imaginary part of the non-trivial zeroes of the Riemann zeta function, assuming the Riemann hypothesis … 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
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## 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
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## Fractional calculus and interpolation of generalized binomial coefficients

Draft Interpolation of the generalized binomial coefficients underlie the representation of a particular class of fractional differintegro operators by convolution integrals and Cauchy-like complex contour integrals.

## Newton Interpolation and the Derivative in Finite Differences

Relations between the normalized Mellin transform (MT) and Newton interpolation (NI) can shed some light on the validity of a finite difference formula for the derivative alluded to in the MathOverflow question MO-Q: Derivative in terms of finite differences. From … Continue reading