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

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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

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The Creation / Raising Operators for Appell Sequences

The Creation / Raising Operators for Appell Sequences is a pdf presenting reps 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 … Continue reading

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Mellin Interpolation of Differential Ops and Associated Infinigens and Appell Polynomials: The Ordered, Laguerre, and Scherk-Witt-Lie Diff Ops

Interpolations of the derivative operator the fundamental ordered op the Laguerre op the shifted Laguerre op and the generalized Scherk-Witt Lie ops to the fractional operators and are consistently achieved using the Mellin transform of the negated e.g.f.s of the … Continue reading

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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

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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.

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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

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