Calculus of Finite Differences.

Jordan, Charles

doi:10.2307/2333783

Cited by 142 publications

(104 citation statements)

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“…More properties of Stirling numbers can be found in, for example, Jordan [8,Chapter 4], Comtet [5], and in the chapter on combinatorial analysis in Abramowitz and Stegun [1, Chapter 24]. Recent interest in Stirling numbers can be found in Butzer et al [3], [4].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Estimates of Stirling Numbers

Temme

1993

Stud Appl Math

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Section: Introductionmentioning

confidence: 99%

Asymptotic Estimates of Stirling Numbers

Temme

1993

Stud Appl Math

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“…This lemma has a close connection with the Stirling numbers of the second kind (see e.g. [8]), and is well-known (see for e.g. [6], p. 4, 0.154, formula 3).…”

Section: Orthonormalization Of Hpmentioning

confidence: 70%

Holomorphic approximation ofL2-functions on the unit sphere inR3

Schepper

Qian

Sommen

et al. 2014

Journal of Mathematical Analysis and Applications

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Abstract:In this paper we construct an embedding of holomorphic functions in two complex variables into the unit ball in R^3. This leads to a closed subspace of the L2-functions on the unit sphere spanned by quaternionic polynomials for which we construct orthonormal bases and study the related convergence properties. Powered by Editorial Manager® and ProduXion Manager® from Aries Systems CorporationHolomorphic approximation of L 2 -functions on the unit sphere in R 3Nele De Schepper, Tao Qian, Frank Sommen and Jinxun WangAbstract. In this paper we construct an embedding of holomorphic functions in two complex variables into the unit ball in R 3 . This leads to a closed subspace of the L2-functions on the unit sphere spanned by quaternionic polynomials for which we construct orthonormal bases and study the related convergence properties.Mathematics Subject Classification (2010). 33C47.

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“…The sums p 1 = q 11 + q 21 + q 31 + q 41 and p 2 = q 12 + q 22 + q 32 + q 42 determine the order of the partial derivatives with respect to x 1 and x 2 . So, the fourth total derivative of the function f (x 1 (t), x 2 (t)) can be written out in general form on the basis of formula (3.2) and Table 3.2, x (4) or finally f x 1 (t), x 2 (t) (4) A comparison has been made with the result obtained from the REDUCE program for symbolic computations with the purpose of checking it up. It has given the same expression for the fourth total derivative of the function e x 1 (t)x 2 (t) .…”

Section: Example the Fourth Derivative Of The Functionmentioning

confidence: 99%

Generalization of the formula of Faa di Bruno for a composite function with a vector argument

Mishkov

2000

International Journal of Mathematics and Mathematical Sciences

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Abstract. The paper presents a new explicit formula for the nth total derivative of a composite function with a vector argument. The well-known formula of Faa di Bruno gives an expression for the nth derivative of a composite function with a scalar argument. The formula proposed represents a straightforward generalization of Faa di Bruno's formula and gives an explicit expression for the nth total derivative of a composite function when the argument is a vector with an arbitrary number of components. In this sense, the formula of Faa di Bruno is its special case. The mathematical tools used include differential operators, polynomials, and Diophantine equations. An example is shown for illustration.

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Calculus of Finite Differences.

Cited by 142 publications

References 0 publications

Asymptotic Estimates of Stirling Numbers

Asymptotic Estimates of Stirling Numbers

Holomorphic approximation ofL2-functions on the unit sphere inR3

Generalization of the formula of Faa di Bruno for a composite function with a vector argument

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