Английская Википедия: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]

<math> \displaystyle \exp(x f^{-1}(t)) = \sum_{n=0}^{\infty} G_n(x;a,b)\frac{t^n}{n!}</math>

where

<math>f(t)=e^{at}(e^{bt}-1)</math> so <math>f^{-1}(t)=\frac{1}{b}\sum_{k=1}^{\infty}\binom{-(b+ak)/b}{k-1}\frac{t^k}{k}</math>

References

  1. Шаблон:Citation
  2. Gould, H. W. (1961), "A series transformation for finding convolution identities", Duke Math. J. Volume 28, Number 2, 193-202.


Шаблон:Polynomial-stub