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Mathematica > Mathematics and Algorithms > Mathematical Functions > Special Functions > q Functions >

Built-in Mathematica Symbol

QPochhammer

QPochhammer[a, q, n]
gives the

-Pochhammer symbol

QPochhammer[a, q]
gives the

-Pochhammer symbol

QPochhammer[q]
gives the

-Pochhammer symbol

Generate partition numbers:

Generate partition numbers:

Evaluate for complex arguments:

Evaluate to arbitrary precision:

The precision of the input tracks the precision of the output:

Finite products evaluate for all Gaussian rational numbers:

q-series are building blocks of other q-factorial functions:

Build q-analogs of sine and cosine:

q-analog of

Triple product identity:

Find RamanujanTau from it's generating function:

Hirschhorn's modular identity $(TemplateBox[{q, q}, QPochhammer2])^5=TemplateBox[{{q, ^, 5}, {q, ^, 5}}, QPochhammer2] mod 5$ :

Boundary of the unit circle contains a dense subset of essential singularieities of