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# Tag Archives: Infinitesimal generators

## 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

Posted in Math, Uncategorized
Tagged Bernoulli numbers, Burgers' equation, Chebyshev polynomials, Combinatorics, Compositional inverse, Differential operators, Elliptic curves, Elliptic formal group law, Elliptic genera, Enumerative combinatorics, Euler numbers, Eulerian numbers, Evolution equations, Faber polynomials, Geodesics of Virasoro-Bott group, Grassmann polynomials, Grassmannian, Heat equation, Hyperbolic tangent, Infinigens, Infinitesimal generators, KdV, Korteweg-de Vries equation, L-genus, Lie algebra, Lucas (Cardan) polynomials, Refined Eulerian numbers, Riccati, Schwarzian derivative, SL2, Solitons, Swiss knife polynomials, Viscous Burgers equation
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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

Posted in Math
Tagged Appell sequences, Associated Laguerre polynomials, Bell polynomials, Confluent hypergeometric functions, Convolution operators, Creation and annihilation operators, Cycle index polynomials, Differential operators, Digamma function, Falling factorials, Fractional calculus, Gamma classes, Gamma genus, Infinitesimal generators, Inverse Mellin transform, Mellin transform, Psi function, Raising and lowering operators, Riemann zeta function, Rising factorials, Umbral calculus, Umbral compositional inverse pair
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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

Posted in Math
Tagged Associated Laguerre polynomials, Dedekind eta function, Infinitesimal generators, Iterated derivatives, Lie groups and algebra, Lie Witt algebra, Linear fractional transformations, Lower triangular matrices, Mobius transformations, Number triangles, Operator calculus, Pascal triangle, SL2, Vector fields
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