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Applied Mathematics and Computation, ISSN 0096-3003, 03/2011, Volume 217, Issue 13, pp. 6286 - 6295
A new algorithm for computing the multivariate Faà di Bruno's formula is provided. We use a symbolic approach based on the classical umbral calculus that turns... 
Faà di Bruno's formula | Multivariate Hermite polynomial | Multivariate cumulant | Multivariate composite function | Classical umbral calculus | POLYNOMIALS | MATHEMATICS, APPLIED | DIBRUNO,FAA | Faa di Bruno's formula | CUMULANTS | Mathematical models | Calculus | Algorithms | Computation | Mathematical analysis
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 03/2010, Volume 59, Issue 6, pp. 2047 - 2052
The well-known formula of Faà di Bruno's for higher derivatives of a composite function has played an important role in combinatorics. In this paper we... 
Divided difference | Bell polynomial | Faà di Bruno's formula | Multicomposite function | MATHEMATICS, APPLIED | DIBRUNO,FAA FORMULA | Faa di Bruno's formula | DERIVATIVES
Journal Article
2017, Synthesis lectures on visual computing: computer graphics, animation, computational photography, and imaging, ISBN 9781627059053, Volume 25, xv, 233 pages
This book is written for students, CAD system users and software developers who are interested in geometric continuity-a notion needed in everyday practice of... 
Geometry, Differential | Computing and Processing | General Topics for Engineers
Book
Discrete Mathematics, ISSN 0012-365X, 03/2011, Volume 311, Issue 6, pp. 387 - 392
Fa di Bruno's formula is the higher chain rule for differentiation. By means of Gessel's q-composition we derive a q-analogue of Fa di Bruno's determinant... 
q-analogue | Complete Bell polynomial | Fa di Bruno's formula | Determinant | MATHEMATICS | DIVIDED DIFFERENCE FORM | Faa di Bruno's formula | Bells | Composite functions | Mathematical analysis | Chains | Determinants | Derivatives | Differentiation
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 05/2015, Volume 258, pp. 597 - 607
In the paper, the authors first inductively establish explicit formulas for derivatives of the arc sine function, then derive from these explicit formulas... 
Derivative | Bell polynomial | Elementary function | Explicit formula | Faá di Bruno formula | MATHEMATICS, APPLIED | Faa di Bruno formula | STIRLING NUMBERS | BERNOULLI | 2ND KIND | FORMULAS
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 04/2007, Volume 76, Issue 258, pp. 867 - 877
In this paper we derive two formulas for divided differences of a function of a function. Both formulas lead to other divided difference formulas, such as... 
Integers | Interpolation | Composite functions | Product rule | Quotient rule | Chain rule | Polynomials | Mathematical functions | Coefficients | Divided differences | Faà di Bruno's formula | INTERPOLATION | MATHEMATICS, APPLIED | chain rule | Faa di Bruno's formula | divided differences
Journal Article
Turkish Journal of Mathematics, ISSN 1300-0098, 2014, Volume 38, Issue 3, pp. 558 - 575
We give moment equalities for sums of independent and identically distributed random variables including, in particular, centered and specifically symmetric... 
Bootstrap | Faà di bruno's chain rule | Integer partitions | Marcinkiewicz-Zygmund inequalities | Moments | Self-normalized sums | MATHEMATICS | Faa. di Bruno's chain rule | bootstrap | integer partitions | self-normalized sums
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 01/2020, Volume 272, pp. 90 - 99
In the paper we introduce and study partitions of vectors in Np, as a natural extension of the classical partitions of integers. We show that these vector... 
Multi-dimensional Bell polynomials | Vector partitions | Multi-dimensional Faà di Bruno formulae | MATHEMATICS, APPLIED | Multi-dimensional Faa di Bruno formulae | Partitions | Polynomials | Algorithms | Mathematical analysis | Combinatorial analysis | Mathematics | Computer Science | Classical Analysis and ODEs | Discrete Mathematics
Journal Article
Complex Analysis and Operator Theory, ISSN 1661-8254, 2/2016, Volume 10, Issue 2, pp. 409 - 435
We show that Faà di Bruno’s formula can play important roles in modular forms theory and in the study of differential operators of the form $$ \displaystyle... 
Lagrange inversion formula | Operator Theory | Modular forms | Analysis | Mathematics, general | Eisenstein series | Mathematics | Faà di Bruno’s formula | Complex Variables | Functional Analysis | Classical Analysis and ODEs
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 10/2016, Volume 13, Issue 5, pp. 2795 - 2800
In the paper, the author finds an explicit formula for the Bell numbers in terms of the Lah numbers and the Stirling numbers of the second kind. 
Lah number | Faà di Bruno formula | Secondary 11B75 | 26A24 | 33B10 | Mathematics | derivative | exponential function | Primary 11B73 | Bell number | Bell polynomial | Explicit formula | Mathematics, general | Stirling number of the second kind | MATHEMATICS | MATHEMATICS, APPLIED | Faa di Bruno formula
Journal Article
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 1/2019, Volume 113, Issue 1, pp. 1 - 9
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 10/2019, Volume 223, Issue 10, pp. 4191 - 4225
Differential categories were introduced by Blute, Cockett, and Seely as categorical models of differential linear logic and have since led to abstract... 
Faà di Bruno formula | Hurwitz series rings | Differential categories | Differential algebras | FORMS | MATHEMATICS | MATHEMATICS, APPLIED | MODELS | Faa di Bruno formula | Analysis | Algebra | Mathematics - Category Theory
Journal Article
Theoretical Population Biology, ISSN 0040-5809, 06/2008, Volume 73, Issue 4, pp. 543 - 551
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 8
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2005, Volume 148, Issue 3, pp. 246 - 255
The coefficients of g ( s ) in expanding the rth derivative of the composite function g ∘ f by Faà di Bruno's formula, is determined by a Diophantine linear... 
Diophantine equations with lower and upper bounds | Knapsack systems | Integer partitions | Lattices | Derivatives of composite functions | derivatives of composite functions | MATHEMATICS, APPLIED | diophantine equations with lower and upper bounds | FAA | COMPOSITE FUNCTIONS | lattices | DERIVATIVES | integer partitions
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2014, Volume 260, pp. 201 - 207
Guo and Qi (2013) posed a problem asking to determine the coefficients ak,i−1 for 1≤i≤k such that 1/(1−e−t)k=1+∑i=1kak,i−1(1/(et−1))(i−1). The authors answer... 
Fubini number | Faà di Bruno’s formula | Apostol–Bernoulli number | Exponential function | Stirling number | Explicit expression | Q-ANALOG | MATHEMATICS, APPLIED | Apostol-Bernoulli number | Faa di Bruno's formula | APOSTOL-BERNOULLI | DI-BRUNOS FORMULA | Exponential functions | Mathematical models | Computation | Mathematical analysis | Combinatorial analysis
Journal Article
Topology and its Applications, ISSN 0166-8641, 02/2018, Volume 235, pp. 375 - 427
In this paper, we consider abelian functor calculus, the calculus of functors of abelian categories established by the second author and McCarthy. We carefully... 
Abelian categories | Faà di Bruno formula | Chain rule | Functor calculus | Cartesian differential categories | MATHEMATICS | MATHEMATICS, APPLIED | Faadi Bruno formula
Journal Article
by Pan, Y and Wang, M
Complex Variables and Elliptic Equations, ISSN 1747-6933, 02/2008, Volume 53, Issue 2, pp. 159 - 175
We study the singular behaviour of k-th angular derivatives of analytic functions in the unit disk in the complex plane ℂ and positive harmonic functions in... 
Angular derivatives | Faà di Bruno's formula | Positive harmonic functions | MATHEMATICS | Faa di Bruno's formula
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 2003, Volume 16, Issue 6, pp. 975 - 979
A short proof of the generalized Faa di Bruno formula is given and an explicit parametrization of the set of indices involved in the coefficient of a specific... 
Differential calculus | Composite functions | Partial derivatives | composite functions | differential calculus | MATHEMATICS, APPLIED | partial derivatives | DERIVATIVES | BRUNO,FAA,DI FORMULA
Journal Article
The ANZIAM Journal, ISSN 1446-1811, 1/2007, Volume 48, Issue 3, pp. 327 - 341
Journal Article
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