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In [[mathematics]] the '''Gould polynomials''' ''G''<sub>''n''</sub>(''x''; ''a'',''b'') are [[polynomial]]s introduced by H. W. Gould and named by Roman in 1984.<ref>{{Citation | last1=Roman | first1=Steven | title=The umbral calculus | url=http://books.google.com/books?id=JpHjkhFLfpgC | publisher=Academic Press Inc. [[Harcourt (publisher)|Harcourt Brace Jovanovich Publishers]] | location=London | series=Pure and Applied Mathematics | isbn=978-0-12-594380-2 | mr=741185 |id=Reprinted by Dover, 2005 | year=1984 | volume=111}}</ref> | |||
They are given by <ref>Gould, H. W. (1961), "A series transformation for finding convolution identities", ''Duke Math. J.'' Volume 28, Number 2, 193-202.</ref> | |||
:<math> \displaystyle \exp(xf(t)) = \sum_nG_n(x;a,b)t^n/n!</math> | |||
where | |||
:<math>f(t)=\sum_{k\ge 1} \frac{1}{b}\binom{-(b+ak)/b}{k-1}\frac{t^k}{k!}</math> | |||
==References== | |||
<references/> | |||
[[Category:Polynomials]] | |||
Revision as of 21:34, 3 January 2014
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]
where
References
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