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BellB

BellB[n]
gives the Bell number .
BellB
gives the Bell polynomial .
  • 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.
The tenth Bell number:
The fifth Bell polynomial:
The tenth Bell number:
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The fifth Bell polynomial:
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Click for copyable input
Out[1]=
Evaluate numerically:
The precision of the output tracks the precision of the input:
BellB threads element-wise over lists:
TraditionalForm formatting:
BellB can be applied to a power series:
BellB numbers versus their asymptotics:
Compute the first 10 :
Generating function:
Sum can give results involving BellB:
Use FullSimplify to simplify expressions involving BellB:
Compute Bell numbers directly from set partitions:
Compute Bell numbers using generalized Bell polynomials:
The first argument of BellB must be a non-negative integer:
Integral representation for Bell numbers by Cesàro:
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