Generating functions
Thomas Baruchel
baruchel at bluebottle.com
Wed Nov 23 18:04:35 CET 2005
Hi,
f(x) being a rational function :
(a x^k + b x^(k-1) + ...) / (e x^l + f x^(l-1) + ... )
the expansion of f(x) is very easy to compute. I have the following
questions concerning the expansion of such a function :
a) is there a sufficient criterion for having no null coefficient ?
Of course in the definition of f(x), the numerator must have
a term of degree 0 being not null (if this term is null, initial
terms in the expansion will also be null), but it is not sufficient:
1/(-x^2 + 1) has [1,0,1,0,1,0,1,0,1,...] in its expansion.
b) is there a sufficient criterion for having an increasing sequence
in the expansion (initial terms don't matter) ?
Same question with the absolute value of the terms.
c) is there a sufficient criterion for having some control on
the sign of the terms (all positive, alternate, etc.) ?
Regards,
--
Thomas Baruchel
Home Page: http://baruchel.free.fr/~thomas/
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