Gould polynomials

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In mathematics the Gould polynomials Gn(x; a,b) are polynomials introduced by H. W. Gould and named by Roman in 1984.[1] They are given by [2]

Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \displaystyle \exp(xf(t)) = \sum_nG_n(x;a,b)t^n/n!

where

Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): f(t)=\sum_{k\ge 1} \frac{1}{b}\binom{-(b+ak)/b}{k-1}\frac{t^k}{k!}


References

  1. Lua error in package.lua at line 80: module 'strict' not found.
  2. Gould, H. W. (1961), "A series transformation for finding convolution identities", Duke Math. J. Volume 28, Number 2, 193-202.