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# Tag Archives: Inverse Mellin transform

## 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

## Differential Ops, Special Polynomials, Binomial Transforms, Interpolation, and the Inverse Mellin Transform

Differential Ops, Special Polynomials, Binomial Transforms, Interpolation, and the Inverse Mellin Transform: (pdf, under construction. ) Relations between differential operators represented in the two basis sets and and the underlying binomial transforms of the associated coefficients of the pairs of … Continue reading

Posted in Math
Tagged Associated Laguerre polynomials, Bell polynomials, Binomial transform, Differential operators, Euler transformations, Falling factorials, Finite differences, Generalized Dobinski relation, Inverse Mellin transform, Mellin transform, Modular forms and eigenfunctions, Newton interpolation, Number operator, Permutahedra face polynomials, Stirling numbers of the second kind, Touchard polynomials, Umbral composition
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## Riemann’s Jump Function J(x) for the Primes

Dirac’s Delta Function and Riemann’s Jump Function J(x) for the Primes presents Riemann’s jump function for counting the primes as introduced in H. M. Edward’s Riemann’s Zeta Function (Dover, 2001), couched in terms of the Dirac delta function and the inverse Mellin transform.