Related papers: Complex branches of a generalised Lambert $W$ func…
In this paper we consider structures of complex Poisson brackets on the space of smooth functions in a $n$-dimensional complex manifold generated by the $(1,1)$-form $d=\partial+\overline{\partial}$-closed and non-degenerate (with…
In this paper, we introduce and investigate a novel subclass $\Sigma(\theta, \lambda, \gamma)$ of meromorphic functions defined in the punctured unit disk ${D}^*$. This class is constructed utilizing a specialized generalized operator…
Functional methods and a derivative expansion are employed for laying out a procedure to compute the effective action to any loop order, for scalar fields parametrising an arbitrary Riemannian manifold, while maintaining explicit…
The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the 't Hooft expansion for matrix integral, these solutions are described by…
Let $\{\Omega_t:-1<t<1\}$ be a family of bounded pseudoconvex domains and $\varphi_t\in PSH(\Omega_t)$. Let $K_t(z,w)$ denote the Bergman kernel with weight $\varphi_t$ on $\Omega_t$. We study the continuity and H\"older continuity of…
Our concern is with Riemannian symmetric spaces $Z=G/K$ of the non-compact type and more precisely with the Poisson transform $\mathcal{P}_\lambda$ which maps generalized functions on the boundary $\partial Z$ to $\lambda$-eigenfunctions on…
This paper continues earlier work where an explicit parametrized solution of a particular nonlinear ordinary differential equation was obtained in terms of the Weierstrass elliptic phi-function, sigma function and zeta function -- work…
We derive the expressions for $\psi$-functions and generic solutions of lattice principal chiral equations, lattice KP hierarchy and hierarchy including lattice N-wave type equations. $\tau$-function of $n$ free fermions plays fundamental…
We study an integro-differential equation which generalizes the periodic intermediate long wave (ILW) equation. The kernel of the singular integral involved is an elliptic function written as a second order difference of the Weierstrass…
In this paper, we study the Lambert-Tsallis function, which is a generalization of the Lambert function with two real parameters. We give a condition on the parameters such that there exists a complex domain touching zero on boundary which…
Our purpose in this present paper is to investigate generalized integration formulas containing the generalized $k$-Bessel function $W_{v,c}^{k}(z)$ to obtain the results in representation of Wright-type function. Also, we establish certain…
I present a new way to solve the Wheeler--de Witt equation using the invariance of the classical lagrangian under reparametrization. This property allows one to introduce an arbitrary function for each degree of freedom of the wave function…
A modular relation of the form $F(\alpha, w)=F(\beta, iw)$, where $i=\sqrt{-1}$ and $\alpha\beta=1$, is obtained. It involves the generalized digamma function $\psi_w(a)$ which was recently studied by the authors in their work on developing…
We obtain some new properties of the signal generated by the Riemann zeta-function in this paper. Namely, we show the connection between the function $\zf$ and a nonlinear integral equation related to the Poisson-Lobachevsky integral.
This paper proposes an approach of the unified consideration of classical and quantum mechanics from the standpoint of the complex analysis effects. It turns out that quantization can be interpreted in terms of the Riemann surface…
We consider a generalisation of a definite integral involving the Bessel function of the first kind. It is shown that this integral can be expressed in terms of the Fox-Wright function ${}_p\Psi_q(z)$ of one variable. Some consequences of…
A new approach is presented for the calculation of p_n and pi_n which uses the Lambert W function. An approximation is first found and using a calculation technique it makes it possible to have an estimate of these two quantities more…
Some diophantine problems are stated for the Omega constant and, more generally, the values of Lambert $W$-function and their $p$-adic extensions.
We establish Sobolev-Poincar\'e inequalities for piecewise $W^{1,p}$ functions over families of fairly general polytopic (thence also shape-regular simplicial and Cartesian) meshes in any dimension; amongst others, they cover the case of…
We present a new approach to examine transient dynamics in a class of non-autonomous delay differential equations. Exact solutions for these equations are obtained using the Lambert W function alongside an appropriately chosen initial…