QPochhammer
QPochhammer[a,q,n]
gives the -Pochhammer symbol
.
QPochhammer[a,q]
gives the -Pochhammer symbol
.
QPochhammer[q]
gives the -Pochhammer symbol
.
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
.
.
- QPochhammer automatically threads over lists.
Examples
open allclose allBasic Examples (4)
Scope (20)
Numerical Evaluation (4)
Specific Values (4)
Values of QPochhammer at fixed points:
QPochhammer for symbolic parameters:
Finite products evaluate for all Gaussian rational numbers:
Find the maximum of QPochhammer[x]:
Visualization (2)
Function Properties (9)
Approximate function range of :
Has both singularities and discontinuities for x≤-1 or for x≥1:
is neither nonincreasing nor nondecreasing:
QPochhammer is not injective:
QPochhammer is not surjective:
QPochhammer is neither non-negative nor non-positive:
QPochhammer is neither convex nor concave:
TraditionalForm formatting:
Series Expansions (1)
Find the Taylor expansion using Series:
Applications (5)
-series are building blocks of other
-factorial functions:
Build -analogs of sine and cosine:
Verify some analogs of the usual trigonometric identities:
Find RamanujanTau from its generating function, the modular discriminant:
Text
Wolfram Research (2008), QPochhammer, Wolfram Language function, https://reference.wolfram.com/language/ref/QPochhammer.html.
CMS
Wolfram Language. 2008. "QPochhammer." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/QPochhammer.html.
APA
Wolfram Language. (2008). QPochhammer. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/QPochhammer.html