# Bell Polynomials of the Second Kind 1.0

OS : Windows / Linux / Mac OS / BSD / Solaris

Script Licensing : Freeware

Created : Aug 27, 2007

Downloads : 6

Thank you for voting...

## Given a list of input values (x_{1},x_{2},...,x_{N}), ...

Given a list of input values (x_{1}, x_{2}, . . . , x_{N}), the script returns a matrix of Bell polynomials B_{n, k} for n=0, . . . , N and k=0, . . . , K.

where

B_{n, k} = OutMatrix(n 1, k 1)

n=0, . . . , Nin

k=0, . . . , Kin (Kin1

B_{0, k} = 0; for k=>1

The coefficients can be stored in a lower triangular matrix. The elements of the kth column are the Taylor coefficients of the kth derivative of g(t)/k!.

In application, the polynomials arise in multiple contexts in combinatorics. They also can be found in Riordan's formulation of di Bruno's formula for computing an arbitrary order derivative of the composition of two functions

frac{d^{n}}{dt^{n}} g(f(t)) = sum_{k=0}^{n} g^{k}(f(t)) B_{n, k}(f^{1}(t), f^{2}(t), . . . , f^{n-k 1}(t))

**Syntax:**

OutMatrix = bell(Nin, Kin, DataList)where

B_{n, k} = OutMatrix(n 1, k 1)

n=0, . . . , Nin

k=0, . . . , Kin (Kin1

B_{0, k} = 0; for k=>1

The coefficients can be stored in a lower triangular matrix. The elements of the kth column are the Taylor coefficients of the kth derivative of g(t)/k!.

In application, the polynomials arise in multiple contexts in combinatorics. They also can be found in Riordan's formulation of di Bruno's formula for computing an arbitrary order derivative of the composition of two functions

frac{d^{n}}{dt^{n}} g(f(t)) = sum_{k=0}^{n} g^{k}(f(t)) B_{n, k}(f^{1}(t), f^{2}(t), . . . , f^{n-k 1}(t))

**Script Check:**

If DataList=1 for all entries, B_{n, k} = S(n, k) = Stirling number of the second_kind for (n, k)**Failure Return:**

OutMatrix is undefined if the code fails. An error statement is issued and the function exits.**• MATLAB Release: R2006b**

**Demands:****Bell Polynomials of the Second Kind 1.0 scripting tags:**polynomials, bnk, derivative, bell, bell polynomials, second kind, coefficients, matlab mathematics, kth, matrix.

**What is new in Bell Polynomials of the Second Kind 1.0 software script?**- Unable to find Bell Polynomials of the Second Kind 1.0 news.

**What is improvements are expecting?**Newly-made Bell Polynomials of the Second Kind 1.1 will be downloaded from here. You may download directly. Please write the reviews of the Bell Polynomials of the Second Kind. License limitations are unspecified.