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Generating Functions

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A generating function f(z) for a sequence a0,a1,a2,... of numbers is the power series

f(z) = a0 + a1 z + a2 z2 + ...
Even if there doesn't exist a generating function for the number of groundforms, for every binary form there exists a generating function for the number of lineary independent covariants in each degorder.
For more information see e.g. Fabian Franklin , On the Calculation of the Generating Functions and Tables of Groundforms of Binary Quantics, American Journal of Mathematics, 3, 1880, p. 128-153

You can download the Generating Functions for binary quantics up to the octavic as DVI-, Postscript- or PDF- file. Their reduced form is listed as well as their representing form. More Generating Functions can be computed using the programme franklin.

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