Related papers: An identity for derivatives
A unified explicit form for difference formulas to approximate the fractional and classical derivatives is presented. The formula gives finite difference approximations for any classical derivatives with a desired order of accuracy at nodal…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
We Define moments of partitions of integers, and show that they appear in higher order derivatives of certain combinations of functions.
A recursion formula for derivatives of Chebyshev polynomials is replaced by an explicit formula.
We obtain a new simple formula for the regularized traces of singular ordinary differential operators.
We present an identity for the derivatives of the arctangent function as an alternative to the Adegoke - Layeni - Lampret formula. We show that algorithmic implementation of the proposed identity can significantly accelerate the computation…
From physical perspective, derivatives can be viewed as mathematical idealizations of the linear growth. The linear growth condition has special properties, which make it preferred. The manuscript investigates the general properties of the…
We formulate several polynomial identities. One side of these identities has a nice simple form. Whereas the other has a form of a polynomial whose coefficients contain binomial coefficients double factorials or (and) rising factorials. The…
A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent…
In this note, we prove a quantization formula for singular reductions. The main result is obtained as a simple application of an extended quantization formula proved in [TZ2].
We present and prove a general form of Vandermonde's identity and use it as an alternative solution to a classic probability problem.
This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really…
We give a closed formula for the derivative of arbitrary order of the function $\ds g(x)=\exp(f(x))$.
We use the properties of Hermite and Kamp\'e de F\'eriet polynomials to get closed forms for the repeated derivatives of functions whose argument is a quadratic or higher-order polynomial. The results we obtain are extended to product of…
We give yet another proof for Fa\`{a} di Bruno's formula for higher derivatives of composite functions. Our proof technique relies on reinterpreting the composition of two power series as the generating function for weighted integer…
In this note we compare two formulas for the higher order derivatives of the function 1/(exp(x) -1). We also provide an integral representation for these derivatives and obtain a classical formula relating zeta values and Bernoulli numbers.
We characterize generalized derivatives of the solution operator of the obstacle problem. This precise characterization requires the usage of the theory of so-called capacitary measures and the associated solution operators of relaxed…
In this paper, we first give a simple combinatorial proof of Tepper's identity. Then, as a by product of this interesting identity we present another proof of the well-known Wilson's identity in number theory. Finally, we obtain a…
A generalization of the Catalan numbers is considered. New results include binomial identities, recursive relations and a close formula for the multivariate generating function. A simple expression for the Catalan determinant is derived.
We study the explicit formula of Euler numbers and polynomials of higher order