Monthly Archives: November 2011

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.

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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

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Note on the Inverse Mellin Transform and the Dirac Delta Function.

The use of the Dirac Delta Function allows simple derivations of many common Mellin Transforms. The Mellin Transform and the Dirac Delta Function is a quick note that addresses a question posed on MathOverflow.

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