Q-series

$(a,q)\_n\; =\; \backslash prod\_\{k=0\}^\{n-1\}\; (1-aq^k)$

$\backslash phi(q)=\backslash prod\_\{k=1\}^\backslash infty\; (1-q^k)$

$\backslash frac\{1\}\{\backslash phi(q)\}=\backslash sum\_\{k=0\}^\backslash infty\; p(k)\; q^k$

$\backslash phi(q)=\backslash sum\_\{n=-\backslash infty\}^\backslash infty\; (-)^n\; q^\{(3n^2-n)/2\}$

$\backslash phi(q)=\; q^\{-1/24\}\; \backslash eta(\backslash tau)$

Q-analogues

See also

• Gaussian binomial
• Stirling number
• Young tableau
• Jacobi theta function
• Modular forms

References

• Eugene Mukhin Symmetric Polynomials and Partitions (undated, 2004 or earlier)
• Linas Vepstas Spectral Analysis of Mandelbrot Interior (2000) describes the appearance of q-series in the Mandelbrot Set.

<< Previous Word Browser Next >>
alan rollinson alberto colombo alberto crespo andre testut andy sutcliffe azdrubal fontes bernard de dryver bill moss brian gubby brian mcguire british columbia general election, 1986	bruce kessler carlo facetti carlo franchi claudio langes clive puzey dave kennedy desire wilson emilio zapico enrico bertaggia bandar maharani ernesto brambilla	ernesto prinoth inspector hopkins frank dochnal square pegs gary brabham gianfrance brancatelli giorgio francia giovanni amati gunther seiffert hiroshi fushida jean lucienbonnet	ken kavanagh ken richardson kevin cogon kurt kuhnke luigi taramazzo michael bartels mikko kazarowitsky c7 sport taliesin west naoki hattori otto stuppacher