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based on an earlier version of the Wolfram Language.
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gives the Stirling number of the first kind .
  • Integer mathematical function, suitable for both symbolic and numerical manipulation.
  • gives the number of permutations of elements that contain exactly cycles.
StirlingS1 threads element-wise over lists:
TraditionalForm formatting:
Plot Stirling numbers of the first kind on a logarithmic scale:
Plot the average number of cycles in symmetric group elements:
Generate values from the generating function:
Stirling numbers of the first kind are effectively inverses of Stirling numbers of the second kind:
Calculate large Stirling numbers of the first kind using Cauchy's theorem:
StirlingS1 can have large values for moderately sized arguments:
The value at is defined to be 1:
Plot sums of digits:
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