The Bell functions only evaluate to a polynomial when the arguments specifying the degree are positive integers
A sequence with the values of for
The IncompleteBellB polynomials have a special form for some particular values of the function's parameters. For illustration purposes consider the generic sequence
For and , or and , or , IncompleteBellB is equal to 0
For , the following identity holds
If for all , the following identity holds
If for all , the following identity, here expressed in terms of the inert sequence %seq, holds
The diamond operation that enters the definition of IncompleteBellB can be invoked directly as IncompleteBellB:-DiamondConvolution. These are the first 4 elements of , a diamond operation involving 2 factors
Note that when calling IncompleteBellB:-DiamondConvolution, you pass the sequence enclosed in a list. The value of is equal to the 4th element of the above sequence divided by
These are the first 5 elements of , a diamond operation involving 3 factors and the value of
The value of is obtained by adding the values of for as explained in the Description