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StirlingS2

StirlingS2
gives the Stirling number of the second kind .
  • Integer mathematical function, suitable for both symbolic and numerical manipulation.
  • gives the number of ways of partitioning a set of elements into non-empty subsets.
StirlingS2 threads element-wise over lists:
TraditionalForm formatting:
Plot Stirling numbers of the second kind on a logarithmic scale:
Stirling numbers modulo 2:
Closed form of derivatives of compositions with exponential functions:
Generate values from the generating function:
Stirling numbers of the second kind are effectively inverses of Stirling numbers of the first kind:
Calculate large Stirling numbers of the second kind using Cauchy's theorem:
Generate Stirling numbers of the second kind from the commutation relation :
The limit of finite differences of powers are Stirling numbers of the second kind:
StirlingS2 can take large values for moderate-size arguments:
The value at is defined to be 1:
Plot sums of digits:
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