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Mathematica > Mathematics and Algorithms > Discrete Mathematics > Combinatorial Functions > StirlingS2 >

BUILT-IN MATHEMATICA SYMBOL

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.

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StirlingS2 threads element-wise over lists:

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: