BellB

BellB[n]

gives the Bell number .

BellB[n,x]

gives the Bell polynomial .

Details

  • 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

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Basic Examples  (2)

The tenth Bell number:

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The fifth Bell polynomial:

In[1]:=
Click for copyable input
Out[1]=

Scope  (4)

Generalizations & Extensions  (1)

Applications  (2)

Properties & Relations  (8)

Possible Issues  (1)

Neat Examples  (1)

See Also

StirlingS2  Subsets  PartitionsQ  BellY

Tutorials

Introduced in 2007
(6.0)