Tag Archives: exponential generating function

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

Posted in Math | Tagged , , , , , , , , | Leave a comment

The Kervaire-Milnor Formula

The K-M formula and its ingredients are presented in 1) Bernoulli numbers and the unity of mathematics by Barry Mazur, p.14, Secs. 4, 5, and 6 2) Differential topology forty-six years later by Milnor 3) Homotopy group of spheres Wikipedia … Continue reading

Posted in Math | Tagged , , , , , , , , , , , , , , , | 2 Comments

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

Posted in Math | Tagged , , , , , , , , , , , , | Leave a comment

The Refined Lives of the F- and H-Vectors of Associahedra

The compositional inversions noted in the Oct. 9-th entry “Flipping Functions with Permutohedra” have counterparts with respect to the associahedra, or Stasheff polytopes. The h-polynomials of the simplicial complexes dual to the associahedra (see the Narayana number triangle OEIS-A001263) can … Continue reading

Posted in Math | Tagged , , , , , , , , , , , | Leave a comment