Related papers: Generalization of the Taylor formula
In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.
In this paper we summarize some known facts on slice topology in the quaternionic case, and we deepen some of them by proving new results and discussing some examples. We then show, following [18], how this setting allows us to generalize…
Orientational expansions, which are widely used in the natural sciences, exist in angular and Cartesian form. Although these expansions are orderwise equivalent, it is difficult to relate them in practice. In this article, both types of…
A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…
We establish Taylor series expansions in rational (and elliptic) function bases using E. Rains' elliptic extension of the Askey-Wilson divided difference operator. The expansion theorem we consider extends M.E.H. Ismail's expansion for the…
This note investigates the relation between squeezing function and its generalizations. Using the relation obtained, we present an alternate method to find expression of generalized squeezing function of unit ball corresponding to the…
We introduce generalized notions of a divergence function and a Fisher information matrix. We propose to generalize the notion of an exponential family of models by reformulating it in terms of the Fisher information matrix. Our methods are…
An extensive table of pairs of functions linked by the Legendre transformation is presented. Many special functions and formulas that are used in the sciences are included in the pairs. Formulations are provided for finding the Legendre…
In this paper, we propose a generalization of a congruence due to Carlitz.
The aim of this paper is to derive on the basis of the Euler's formula several analytical relations which hold for certain classes of planar graphs and which can be useful in algorithmic graph theory.
After reviewing some fundamental facts from the theory of theta hypergeometric series we derive, using indefinite summation, several summation, transformation, and expansion formulas for multibasic theta hypergeometric series. Some of the…
Summation formulas, such as the Euler-Maclaurin expansion or Gregory's quadrature, have found many applications in mathematics, ranging from accelerating series, to evaluating fractional sums and analyzing asymptotics, among others. We show…
The paper deals with the generalization of both Boltzmann entropy and distribution in the light of most-probable interpretation of statistical equilibrium. The statistical analysis of the generalized entropy and distribution leads to some…
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
We introduce and study expansions of real numbers with respect to two integer bases.
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.
The long-wavelength approximation and the truncated Taylor expansion are frequently used in the theory of relativistic Coulomb excitation to obtain multipole expansions of the interaction. It is shown in this note that these two…
We formulate a general setting for the cluster expansion method and we discuss sufficient criteria for its convergence. We apply the results to systems of classical and quantum particles with stable interactions.
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
Generalisations of the classical Euler formula to the setting of fractional calculus are discussed. Compound interest and fractional compound interest serve as motivation. Connections to fractional master equations are highlighted. An…