Tag Archives: Associated Laguerre polynomials

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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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

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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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