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Tag Archives: Compositional inverse
From Wikipedia on the LRT, with , . Letting and , and , giving , the Lagrange inversion formula about the origin, whose expansion in the Taylor series coefficients of is discussed in OEIS A248927. See also A134685. For connections … Continue reading
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
The raising op for any Appell sequence is determined by the derivative of the log of the e.g.f. of the basic number sequence, connecting the op to the combinatorics of the cumulant expansion OEIS-127671 of the moment generating function and … Continue reading
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:
Compositional Inverse Pairs, the Inviscid Burgers-Hopf Equation, and the Stasheff Associahedra: A brief note (pdf) on some relations among these topics, including the Catalan and Fuss-Catalan numbers. References are provided linking the analysis with the distribution of eigenvalues of random … Continue reading
Lagrange à la Lah Part I and Lagrange à la Lah Part II are a set of notes on partition polynomials derived from binomial Sheffer sequences via umbral refinement, their relation to compositional inversion via the Laplace transform, and their characterization by umbral … Continue reading
Flipping Functions with Permutohedra : A short note on forming the multiplicative and compositional inverses of functions using the refined Eulerian h-polynomials OEIS-A145271 and refined face polynomials of permutohedra OEIS-A049019.
Short Note on Lagrange Inversion is an addendum to OEIS-A134685.