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Stephen Wolfram
SEARCH MATHEMATICA 8 DOCUMENTATION
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE
DOCUMENTATION CENTER
FOR THE LATEST INFORMATION.
Mathematica
>
Mathematics and Algorithms
>
Discrete Mathematics
>
Combinatorial Functions
>
Mathematica
>
Mathematics and Algorithms
>
Mathematical Functions
>
Integer Functions
>
Combinatorial Functions
>
Built-in
Mathematica
Symbol
BarnesG
Gamma
Glaisher
See Also »
|
Combinatorial Functions
Gamma Functions and Related Functions
Summary of New Features in 7.0
New in 7.0: Alphabetical Listing
New in 7.0: Mathematics & Algorithms
More About »
Hyperfactorial
Hyperfactorial
[
n
]
gives the hyperfactorial function
.
MORE INFORMATION
Mathematical function, suitable for both symbolic and numeric manipulation.
Hyperfactorial is defined as
for positive integers
.
The hyperfactorial function satisfies
.
Hyperfactorial
can be evaluated to arbitrary numerical precision.
Hyperfactorial
automatically threads over lists.
EXAMPLES
CLOSE ALL
Basic Examples
(3)
In[1]:=
Out[1]=
In[1]:=
Out[1]=
In[1]:=
Out[1]=
Scope
(6)
Evaluate numerically:
Evaluate for complex argument:
Evaluate to arbitrary precision:
The precision of the output tracks the precision of the input:
Hyperfactorial
threads element-wise over lists:
TraditionalForm
formatting:
Applications
(1)
The discriminant of the Hermite polynomial is related to the hyperfactorial:
Properties & Relations
(1)
Hyperfactorial
is produced in
Product
:
SEE ALSO
BarnesG
Gamma
Glaisher
MORE ABOUT
Combinatorial Functions
Gamma Functions and Related Functions
Summary of New Features in 7.0
New in 7.0: Alphabetical Listing
New in 7.0: Mathematics & Algorithms
RELATED LINKS
Demonstrations with Hyperfactorial
(
Wolfram Demonstrations Project
)
New in 7
.
for positive integers 
.
.
EXAMPLES
Basic Examples 
Scope 