Related papers: A solution to Ahmed's Integral(II)
While teaching a course on integral equations, I noticed that a straightforward combination of Neumann series and Fourier series for the resolvent (or the solution) of an integral equation has good approximation qualities. This short…
The complexes of integral forms on the quantum Euclidean group $E_q(2)$ and the quantum plane are defined and their isomorphisms with the corresponding de Rham complexes are established.
Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms…
Two results are presented for reduced Yang-Mills integrals with different symmetry groups and dimensions: the first is a compact integral representation in terms of the relevant variables of the integral, the second is a method to…
The (2+1)-dimensional integrable M-XX equation is considered.
We introduce a family of polynomials in $q^2$ and four variables associated with the quantized algebra of functions $A_q(C_2)$. A new formula is presented for the recent solution of the 3D reflection equation in terms of these polynomials…
We find the general hyper-elliptic solutions to the two-component reduced Nahm equations proposed by Hitchin et al. Elliptic solutions are a special case and can appear only for specific values of the monopole charges.
In the framework of bidifferential graded algebras, we present universal solution generating techniques for a wide class of integrable systems.
(Minor corrections and reference added)
We discuss a problem initially thought for the Mathematical Olympiad but which has several interpretations. The recurrence sequences involved in this problem may be generalized to recurrence sequences related to a much larger set of…
We prove a novel type of inversion formula for elliptic hypergeometric integrals associated to a pair of root systems. Using the (A,C) inversion formula to invert one of the known C-type elliptic beta integrals, we obtain a new elliptic…
In 1853 Sylvester introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial subresultants of the monic polynomials associated with these…
The general solutions with free variable to the second-kind Abel equation, a nonlinear ordinary differential equation that has remained unsolved for nearly two centuries, are presented for the first time by using elementary quadrature…
In this paper, we propose a numerical method of computing an Hadamard finite-part integral, a finite value assigned to a divergent integral, with a non-integral power singularity at the endpoint on a half infinite interval. In the proposed…
The present work includes some of the author's original researches on integer solutions of Diophantine liner equations and systems. The notion of "general integer solution" of a Diophantine linear equation with two unknowns is extended to…
By dividing hypergeometric series representations of the inverse sine by sin^-1 (x) and integrating, new double series representations of integers and constants arise. Binomial coefficients and the sine integral are thus combined in double…
Multiplication and exponentiation can be defined by equations in which one of the operands is written as the sum of powers of two. When these powers are non-negative integers, the operand is integer; without this restriction it is a…
We present an integral representation formula for a Dirichlet series whose coefficients are the values of the Liouville's arithmetic function.
The work deals with the existence of solutions of a certain system of quadratic integral equations in H^2(R^d,R^N), d = 2, 3. We demonstrate the existence of a perturbed solution by virtue of a fixed point technique.
We reduce the calculation of the simplest Hodge integrals to some sums over decorated trees. Since Hodge integrals are already calculated, this gives a proof of a rather interesting combinatorial theorem and a new representation of…