Related papers: Explicit Formula for Witten-Kontsevich Tau-Functio…
We derive explicit formulas for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulas are important for problems of thermo- and photo-…
We present an elegant exact formula for the gaugino $\beta$-function in a softly-broken supersymmetric gauge theory, of the form $\beta_M = {\cal O}(\beta_g/g)$, where $\beta_g$ is the gauge $\beta$ function and ${\cal O}$ is a simple…
We give a formula for matrix exponentials and partial fraction decompositions.
An approach to constructing an upper bound for the Riemann-Farey sum is described.
In the paper we find effective formulas for the invariant functions, appearing in the theory of several complex variables, of the elementary Reinhardt domains. This gives us the first example of a large family of domains for which the…
We derive an explicit formula for the general solution of the cubic Szeg\"o equation and of the evolution equation of the corresponding hierarchy. As an application, we prove that all the solutions corresponding to finite rank Hankel…
We give a transformation formula for the ``2nd order'' mock theta function which was recently proposed in connection with the quantum invariant for the Seifert manifold.
A procedure is proposed to construct solutions of the double confluent Heun equation with a determinate behaviour at the singular points. The connection factors are expressed as quotients of Wronskians of the involved solutions. Asymptotic…
We derive a piecewise-linear formula for the rigid representation of a Dynkin quiver of a given dimension vector, and illustrate the formula in several examples.
We consider stochastic versions of the Cauchy exponential functional equation and give a martingale characterization of the general solution.
We formulate and prove a version of the celebrated Coifman-Rochberg-Weiss commutator theorem for the real method of interpolation
A practical method to compute the Riemann zeta function is presented. The method can compute $\zeta(1/2+it)$ at any $\lfloor T^{1/4} \rfloor$ points in $[T,T+T^{1/4}]$ using an average time of $T^{1/4+o(1)}$ per point. This is the same…
In this letter the explicit form of evolution operator for the four atoms Tavis-Cummings model is given.
A very explicit analytic formula of the separability criterion of two-party Gaussian systems is given. This formula is compared to the past formulation of the separability criterion of continuous variables two-party Gaussian systems.
This paper investigates some combinatorial and algebraic properties of a Witt type formula for graphs.
We show how to obtain the difference function of the Weierstrass Zeta function very directly, by choosing an appropriate order of summation for the series defining this function. As a byproduct, we show how to obtain the quasi-modularity of…
The exact exponential Foldy-Wouthuysen transformation operator applicable for a particle with an arbitrary spin is derived. It can be successfully utilized for verifying any Foldy-Wouthuysen transformation method based on the exponential…
This paper shows the Fermi-Dirac Integrals expressed in terms of Riemann and Hurwitz Zeta functions. This is done by defining an auxiliar function that permits rewrite the Fermi-Dirac integral in terms of simpler and known integrals…
We extend the matrix-resolvent method for computing logarithmic derivatives of tau-functions to the Ablowitz--Ladik hierarchy. In particular, we derive a formula for the generating series of the logarithmic derivatives of an arbitrary…
We find a formula that relates the Fourier transform of a radial function on $\mathbf{R}^n$ with the Fourier transform of the same function defined on $\mathbf{R}^{n+2}$. This formula enables one to explicitly calculate the Fourier…