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The differential equation in the external invariant p^2 satisfied by the master integral of the general massive 2-loop 4-denominator self-mass diagram is exploited and the expansion of the master integral at p^2=0 is obtained analytically.…
We present a semi-analytic calculation of the integrated double-emission eikonal function of two massive emitters whose momenta are at an arbitrary angle to each other. This result is needed for extending the nested soft-collinear…
Geminal wavefunctions have been employed to model strongly-correlated electrons. These wavefunctions represent products of weakly-correlated pairs of electrons and reasonable approximations are computable with polynomial cost. In…
By using Poisson's summation formula, we calculate periodic integrals over Gaussian basis functions by partitioning the lattice summations between the real and reciprocal space, where both sums converge exponentially fast with a large…
We obtain integral representations of the $n$-th derivatives of the Bessel functions with respect to the order. The numerical evaluation of these expressions is very efficient using a double exponential integration strategy. Also, from the…
We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for…
We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential…
The purpose of this paper is to use semiclassical analysis to unify and generalize Lp estimates on high energy eigenfunctions and spectral clusters. In our approach these estimates do not depend on ellipticity and order, and apply to…
Schr\"odinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter separations. Asymptotical expansions for energy term and wave function are obtained in the…
The two-electron problem for the helium-like atom/ions in $S$-state is considered. The basis containing the integer powers of $\ln r$, where $r$ is a radial variable of the Fock expansion, is studied. In this basis, the analytic expressions…
We compute all master integrals for massless three-loop four-particle scattering amplitudes required for processes like di-jet or di-photon production at the LHC. We present our result in terms of a Laurent expansion of the integrals in the…
A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the…
Explicitly-correlated F12 methods are becoming the first choice for high-accuracy molecular orbital calculations, and can often achieve chemical accuracy with relatively small gaussian basis sets. In most calculations, the many three- and…
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
We derive a general formula for two-loop counterterms in Effective Field Theories (EFTs) using a geometric approach. This formula allows the two-loop results of our previous paper to be applied to a wide range of theories. The two-loop…
We prove a closed formula for the integral of a power of a single $\psi$-class on strata of $k$-differentials. In many cases, these integrals correspond to intersection numbers on twisted double ramification cycles. Then we conjecture an…
A new class of bivariate poly-analytic Hermite polynomials is considered. We show that they are realizable as the Fourier-Wigner transform of the univariate complex Hermite functions and form a nontrivial orthogonal basis of the classical…
We give the explicit analytic development of any Jack or Macdonald polynomial in terms of elementary (resp. modified complete) symmetric functions. These two developments are obtained by inverting the Pieri formula.
Two-body matrix elements of arbitrary local interactions are written as the sum of separable terms in a way that is well suited for the exchange and pairing channels present in mean-field calculations. The expansion relies on the…
The class of the two-loop massless crossed boxes, with light-like external legs, is the final unresolved issue in the program of computing the scattering amplitudes of 2 --> 2 massless particles at next-to-next-to-leading order. In this…