# Bell Polynomials of the Second Kind 1.0

OS : Windows / Linux / Mac OS / BSD / Solaris
Script Licensing : Freeware
Created : Aug 27, 2007
Downloads : 6
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## 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.
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.
Demands:
• MATLAB Release: R2006b

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.