Tagged Questions
5
votes
3answers
117 views
How to prove it? (one of the Rogers-Ramanujan identities)
Prove the following identity (one of the Rogers-Ramanujan identities) on formal power series by interpreting each side as a generating function for partitions:
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2
votes
1answer
115 views
Closed form for $\sum_{m \geq 1} (-1)^m q^{m(m+1)/2 + m \Delta}$?
Is there a useful closed form for the following series ($|\Delta|$ is a small integer)?
$$f(q,\Delta) =\sum_{m=1}^{\infty} (-1)^m q^{m(m+1)/2 + m \Delta}$$
It is a large-$n$ approximation of the ...
1
vote
1answer
105 views
Interpolation of a sequence of polynomials (viewed in terms of q-analogue powers)
I'm trying to find closed-form expressions for a sequence of coefficients, such that the index of the coefficient occurs as number such that I can later interpolate to fractional indexes as well. ...
