Matches in DBpedia 2014 for { ?s ?p Faà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives, named after Francesco Faà di Bruno (1855, 1857), though he was not the first to state or prove the formula. In 1800, more than 50 years before Faà di Bruno, the French mathematician Louis François Antoine Arbogast stated the formula in a calculus textbook, considered the first published reference on the subject.Perhaps the most well-known form of Faà di Bruno's formula says thatwhere the sum is over all n-tuples of nonnegative integers (m1, …, mn) satisfying the constraintSometimes, to give it a memorable pattern, it is written in a way in which the coefficients that have the combinatorial interpretation discussed below are less explicit:Combining the terms with the same value of m1 + m2 + ... + mn = k and noticing that m j has to be zero for j > n − k + 1 leads to a somewhat simpler formula expressed in terms of Bell polynomials Bn,k(x1,...,xn−k+1):. }
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- Faà_di_Bruno's_formula abstract "Faà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives, named after Francesco Faà di Bruno (1855, 1857), though he was not the first to state or prove the formula. In 1800, more than 50 years before Faà di Bruno, the French mathematician Louis François Antoine Arbogast stated the formula in a calculus textbook, considered the first published reference on the subject.Perhaps the most well-known form of Faà di Bruno's formula says thatwhere the sum is over all n-tuples of nonnegative integers (m1, …, mn) satisfying the constraintSometimes, to give it a memorable pattern, it is written in a way in which the coefficients that have the combinatorial interpretation discussed below are less explicit:Combining the terms with the same value of m1 + m2 + ... + mn = k and noticing that m j has to be zero for j > n − k + 1 leads to a somewhat simpler formula expressed in terms of Bell polynomials Bn,k(x1,...,xn−k+1):".