Tag Archives: Infinigens

An lnfinite Wronskian Matrix, Binomial Sheffer Polynomials, and the Lagrange Reversion Theorem

Form the infinite Wronskian matrix with elements . A generating function for this matrix is with . If , then also , where is a binomial Sheffer sequence of polynomials. Then in this particular case, and so is the product … 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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The Elliptic Lie Triad: KdV and Riccati Equations, Infinigens, and Elliptic Genera

The Elliptic Lie Triad: Riccati and KdV Equations, Infinigens, and Elliptic Genera (This site was not correctly updating, so the notes were transcribed to this pdf.) Addendum to The Elliptic Lie Triad

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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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