Tag Archives: Hurwitz zeta function

The Riemann and Hurwitz zeta functions and the Mellin transform interpolation of the Bernoulli polynomials

This entry (expanding on the Bernoulli Appells entry) illustrates interpolation with the Mellin transform of the Bernoulli polynomials and their umbral inverses, the reciprocal polynomials, giving essentially the Hurwitz zeta function and the finite difference of , both of which … Continue reading

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Bernoulli Appells

The defining characteristic of the Bernoulli numbers operationally is that they are the basis of the unique Appell sequence, the Bernoulli polynomials, that “translate” simply under the generalized binomial transform (Appell property) and satisfy (for an analytic function, such as … Continue reading

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Bernoulli, Blissard, and Lie meet Stirling and the simplices: State number operators and normal ordering

A set of identities that encapsulates relations among the Bernoulli numbers, the Stirling numbers of the first and second kinds, and operators related to the umbral calculus of Blissard and his contemporaries: Decoding:

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