Related papers: A new integral solution of the hypergeometric equa…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
This paper was withdrawn by the authors because it has been supplanted by gr-qc/0311007 and gr-qc/0311038.
We consider the Gauss-Manin differential equations for hypergeometric integrals associated with a family of weighted arrangements of hyperplanes moving parallelly to themselves. We reduce these equations modulo a prime integer $p$ and…
A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.
A new expansion for integral powers of the hypergeometric function corresponding to a special case of the incomplete beta function is summarized, and consequences, including two new sums involving digamma (psi) functions are presented.
General reduction of the elliptic hypergeometric equation to the level of complex hypergeometric functions is described. The derived equation is generalized to the Hamiltonian eigenvalue problem for new rational integrable $N$-body systems…
We derive solvability conditions and closed-form solution for the Weber type integral equation, related to the familiar Weber-Orr integral transforms and the old Weber-Titchmarsh problem (posed in Proc. Lond. Math. Soc. 22 (2) (1924),…
A refinement of the Hardy inequality has been presented by use of superquadratic function.
We consider the ratio of two Gauss hypergeometric functions, in which the parameters of the numerator function differ from the respective parameters of the denominator function by integers. We derive explicit integral representations for…
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
We outline the solution of the Killing spinor equations of the heterotic supergravity. In addition, we describe the classification of all half supersymmetric solutions.
We present an elliptic version of Selberg's integral formula.
In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established.
In this paper, the versions of trigonometric functions of certain known inequalities for hyperbolic ones are proved, and then corresponding inequalities for means are presented.
We propose a method for transformating linear and nonlinear hypersingular integral equations into ordinary differential equations. Linear and nonlinear polyhypersingular integral equations are transformed into partial differential…
When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find…
We provide a new characterization of the logarithmic Sobolev inequality.
We give a new method to prove in a uniform and easy way various transformation formulas for Gauss hypergeometric functions. The key is Jacobi's canonical form of the hypergeometric differential equation. Analogy for $q$-hypergeometric…
We introduce several new identities combining basic hypergeometric sums and integrals. Such identities appear in the context of superconformal index computations for three-dimensional supersymmetric dual theories. We give both analytic…
In this paper, using the theory of the so-called fractional calculus we show that it is possible to easily obtain the solutions for the confluent hypergeometric equation. Our approach is to be compared with the standard one (Frobenius)…