Related papers: Formula for Hermite multivariate interpolation and…
We introduce a one parameter deformation of the Zwegers' $\mu$-function as the image of $q$-Borel and $q$-Laplace transformations of a fundamental solution for the $q$-Hermite-Weber equation. We further give some formulas for our…
In this paper, we study convergence and superconvergence theory of integer and fractional derivatives of the one-point and the two-point Hermite interpolations. When considering the integer-order derivative, exponential decay of the error…
We generalize two-point interpolatory Hermite quadrature to functions with available values and the first (n-1) derivatives at both end points. Armed with integration by parts in the reverse form we provide an elementary derivation of an…
The semi-Lagrangian method using the hybrid-cubic-rational interpolation function [M. Ida, Comput. Fluid Dyn. J. 10 (2001) 159] is modified to a conservative method by incorporating the concept discussed in [R. Tanaka et al., Comput. Phys.…
We present a new formula for divided difference and few new schemes of divided difference tables in this paper. Through this, we derive new interpolation, numerical differentiation and numerical integration formulas with arbitrary order of…
We present a multigrid iterative algorithm for solving a system of coupled free boundary problems for pricing American put options with regime-switching. The algorithm is based on our recently developed compact finite difference scheme…
In this paper, we establish a $q$-integral formula by using the orthogonality relation, and also provide a new proof of the $q$-orthogonality relation for the continuous $q$-ultraspherical polynomials. A new $q$-beta integral with five…
Ohno's relation is a well known formula among multiple zeta values. In this paper, we present its interpolation to complex functions.
The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions…
The paper presents a new formula for the fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as…
Given a straight-line program whose output is a polynomial function of the inputs, we present a new algorithm to compute a concise representation of that unknown function. Our algorithm can handle any case where the unknown function is a…
In this article we will derive a combinatorial formula for the partition function p(n). In the second part of the paper we will establish connection between partitions and q-binomial coefficients and give new interpretation for q-binomial…
Using the Riesz-Feller fractional derivative, we apply the factorization algorithm to the fractional quantum harmonic oscillator along the lines previously proposed by Olivar-Romero and Rosas-Ortiz, extending their results. We solve the…
Let $z_{1},\ldots,z_{K}$ be distinct grid points. If $f_{k,0}$ is the prescribed value of a function at the grid point $z_{k}$, and $f_{k,r}$ the prescribed value of the $r$\foreignlanguage{american}{-th} derivative, for $1\leq r\leq…
Basing on invariant properties of universal multifractals we propose a simple algorithm for interpolation of multifractal densities. The algorithm admits generalization to a multidimensional case. Analitically obtained are multifractal…
In this paper, first we have established Hermite- Hadamard's inequalities for preinvex functions via fractional integrals. Second we extend some estimates of the right side of a Hermite- Hadamard type inequality for preinvex functions via…
A fractional Adomian decomposition method for fractional nonlinear differential equations is proposed. The iteration procedure is based on Jumarie's fractional derivative. An example is given to elucidate the solution procedure, and the…
In this paper, we find new integral representations for the generalized Hermite linear functional in the real line and the complex plane. As an application, new integral representations for the Euler Gamma function are given.
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration in Almkvist and Zeilberger's framework of (differential) creative telescoping. Our complexity-driven approach is to obtain…