Tag Archives: Operator calculus

Compositional Inverse Operators and Sheffer Sequences

When considering operator inverses, one usually considers multiplicative inverses. As noted earlier in several entries, particularly, “Bernoulli and Blissard meet Stirling … ” (BBS), we see compositional inverse pairs of operators playing an important role in making associations among important … Continue reading

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Dirac-Appell Sequences

The Pincherle derivative  is implicitly used in Eqn. 2.19 page 13 of “Mastering the master field” by Gopakumar and Gross. The raising and creation operators in the paper are analogous to those for a Laplace-dual Appell sequence, or Dirac-Appell sequence, … 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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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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Goin’ with the Flow: Logarithm of the Derivative

Goin’ with the Flow: Logarithm of the Derivative Operator is a pdf set of notes under construction on the relations between the commutator of the logarithm of the derivative operator, the Pincherle derivative,  Lie operator derivatives, and the two umbrally inverse … Continue reading

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Fractional Calculus, Interpolation, and Traveling Waves

Fractional Calculus, Interpolation, and Traveling Waves: A note (pdf file) on the fractional integro-derivative (FID) regarded as an interpolation of the integral derivatives of the function acted upon–to be more precise, a sinc function interpolation, as in the Whittaker-Shannon interpolation … Continue reading

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Infinigens, the Pascal Triangle, and the Witt and Virasoro Algebras

Infinitesimal Generators, the Pascal Pyramid, and the Witt and Virasoro Algebras: A short set of notes sketching some relationships among infinitesimal generators represented as differential operators and infinite-dimensional matrices, the Pascal triangle / pyramid, conformal transformations, the Witt and Virasoro … Continue reading

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