Polynomial Generating Functions/Pascal Matrices
Would anybody be interested in discussing a presentation here on using Pascal/Shift matrices to
directly generate various Polynomial sequences via. their generating functions expressed in matrices?
The underlying idea is that most generating functions are still true when indexing variables (t) are replaced with full rank singular matrices (i.e. n-1). In particular the Pascal or Shift matrices. This leads to the generating function expressed in terms of matrices and most familiar generating functions directly stating the polynomials. Also that the series is truncated automatically and exactly.
I do have some theorems rather than just words :)
I have a "blog" where I have stuffed some notes and results.
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