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.

DetailsDetails

  • 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 Faa 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.
Introduced in 2010
(8.0)