BellY

BellY[n,k,{x1,,xn-k+1}]

gives the partial Bell polynomial .

BellY[n,k,m]

gives the generalized partial Bell polynomial of a matrix m.

BellY[m]

gives the generalized Bell polynomial of a matrix m.

Details

  • Mathematical function, suitable for both symbolic and numeric manipulations.
  • The BellY polynomial is given by Boole[m1+2 m2++n mnnm1+m2++mnk] (xs/s!)ms.
  • The partial Bell polynomial can be used to express the ^(th) derivative of a composition of two functions through the Faà di Bruno formula .
  • The generalized Bell polynomial can be used to express the ^(th) derivative of a composition of functions .
  • BellY[n,k,m] is equivalent to BellY[] where is formed by adding UnitVector[n,k] to m as a first column.

Examples

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Basic Examples  (3)

Partial Bell polynomial:

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Generalized partial Bell polynomial:

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Generalized Bell polynomial:

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Scope  (1)

Applications  (8)

Properties & Relations  (3)

Neat Examples  (1)

See Also

D  BellB  StirlingS2

Introduced in 2010
(8.0)