Related papers: An identity for derivatives
The Riemann-Liouville formula for fractional derivatives and integrals (differintegration) is used to derive formulae for matrix order derivatives and integrals. That is, the parameter for integration and differentiation is allowed to…
Multiple scalar integral representations for traces of operator derivatives are obtained and applied in the proof of existence of the higher order spectral shift functions.
In this paper, a new identity for differentiable functions is derived. Thus we can obtain new estimates on generalization of Hadamard,Ostrowski and Simpson type inequalities for functions whose derivatives in absolute value at certain power…
In a recent paper, Adamchik [V.S. Adamchik, On the Hurwitz function for rational arguments, Appl. Math. Comp. 187 (2007) 3--12] expressed in a closed form symbolic derivatives of four functions belonging to the class of functions whose…
By applying the derivative operator to the corresponding hypergeometric form of a $q$-series transformation due to Andrews [1,Theorem 4], we establish a general harmonic number identity. As the special cases of it, several interesting…
As the title suggests, we give a formula for the $n^{th}$ derivative of a quotient of two functions, analogous to Leibniz's formula for the product. This particular note has remained unpublished since 2007 (available only my website),…
In this work it is propose an alterative proof of one of basic properties of the zonal polynomials. This identity is generalised for the Jack polynomials.
We extend to several variables an earlier result of ours, according to which an entire function of one variable of sufficiently small exponential type, having all derivatives of even order taking integer values at two points, is a…
A conjecture for higher order separation on generic rational surfaces with some new results about standard divisors.
We consider the operator of taking the $2p$th derivative of a function with zero boundary conditions for the function and its first $p-1$ derivatives at two distinct points. Our main result provides an asymptotic formula for the eigenvalues…
We generalize Jacod's condition and introduce a new type sufficient condition for the uniform integrability of the general stochastic exponential.
The well-known mathematical instrument for detection common roots for pairs of polynomials and multiple roots of polynomials are resultants and discriminants. For a pair of polynomials $f$ and $g$ their resultant $R(f,g)$ is a function of…
We consider some possible approaches to the fractional-order generalization of definition of variation (functional) derivative. Some problems of formulation of a fractional-order variational derivative are discussed. To give a consistent…
We consider general subordination and obtain the formula of the subordinated predictable compensator. An example of application is given.
We prove a variation of Gronwall's lemma.
High-order derivatives of nested functions of a single variable can be computed with the celebrated Fa\`a di Bruno's formula. Although generalizations of such formula to multiple variables exist, their combinatorial nature generates an…
In this article, we prove a decomposition theorem on differential polynomials of theta functions of high level.
We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct new summation formulas…
As a generalization of [KMW], we introduce a higher Riemann zeta function for an abstract sequence. Then we explicitly determine its regularized product expression.
By studying the existing higher order derivation formulas of rational B\'{e}zier curves, we find that they fail when the order of the derivative exceeds the degree of the curves. In this paper, we present a new derivation formula for…