PRODUCTS
Mathematica
Mathematica for Students
Mathematica for the Classroom
Mathematica Personal Grid Edition
grid
Mathematica
web
Mathematica
Mathematica Player
(free download)
Mathematica Player Pro
Wolfram
Workbench
Mathematica
Applications
PURCHASE
Online Store
Other Ways to Buy
Volume & Site Licensing
Contact Sales
Software
Service
Upgrades
Training
Books
FOR USERS
All User Resources
Product Registration
Technical Support
Customer Service
Developer Support
Does My Site Have a License?
Free Seminars
Certified Training
Documentation & Examples
Tutorial Screencasts
Video Gallery
Demonstrations Project
Education Portal
Student Resources
COMPANY
About Wolfram Research
News & Events
Wolfram Blog
Employment Opportunities
History of
Mathematica
Stephen Wolfram's Home Page
Contact Us
OUR SITES
Demonstrations Project
MathWorld
Integrator
Wolfram Functions Site
Wolfram Blog
Mathematica Journal
Wolfram Library Archive
Wolfram
Tones
Wolfram Science
Stephen Wolfram
DOCUMENTATION CENTER SEARCH
Mathematica
>
Combinatorial Functions
>
Built-in
Mathematica
Symbol
Combinatorial Functions
Tutorials »
|
StirlingS2
Subsets
PartitionsQ
See Also »
|
Combinatorial Functions
Integer Functions
Number Theoretic Functions
Recurrence and Sum Functions
New in 6.0: Mathematical Functions
New in 6.0: Mathematics & Algorithms
New in 6.0: Number Theory & Integer Functions
More About »
BellB
BellB
[
n
]
gives the Bell number
.
BellB
[
n
,
x
]
gives the Bell polynomial
.
MORE INFORMATION
Mathematical function, suitable for both symbolic and numerical manipulation.
The Bell polynomials satisfy the generating function relation
.
The Bell numbers are given by
.
For certain special arguments,
BellB
automatically evaluates to exact values.
BellB
can be evaluated to arbitrary numerical precision.
BellB
automatically threads over lists.
EXAMPLES
CLOSE ALL
Basic Examples
(2)
The tenth Bell number:
In[1]:=
Out[1]=
The fifth Bell polynomial:
In[1]:=
Out[1]=
Scope
(4)
Generalizations & Extensions
(1)
Applications
(2)
Properties & Relations
(4)
Possible Issues
(1)
SEE ALSO
StirlingS2
Subsets
PartitionsQ
TUTORIALS
Combinatorial Functions
MORE ABOUT
Combinatorial Functions
Integer Functions
Number Theoretic Functions
Recurrence and Sum Functions
New in 6.0: Mathematical Functions
New in 6.0: Mathematics & Algorithms
New in 6.0: Number Theory & Integer Functions
New in 6
© 2008 Wolfram Research, Inc.