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

BUILT-IN MATHEMATICA SYMBOL

QPochhammer

gives the

-Pochhammer symbol

QPochhammer

gives the

-Pochhammer symbol

QPochhammer[q]
gives the

-Pochhammer symbol

MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

QPochhammer automatically threads over lists.

EXAMPLES

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Basic Examples (3)

Generate partition numbers:

Out[1]=

Out[2]=

Out[3]=

Out[1]=

Generate partition numbers:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Scope (5)

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:

TraditionalForm formatting:

Applications (5)

-series are building blocks of other

-factorial functions:

Build

-analogs of sine and cosine:

-analog of

Triple product identity:

Find RamanujanTau from its generating function:

Neat Examples (2)

Hirschhorn's modular identity

The boundary of the unit circle contains a dense subset of essential singularities of