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GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
We present the Gel’fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems of the Feynman integrals of the three-loop vacuum diagrams with arbitrary...
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Feynman integrals in two dimensions and single-valued hypergeometric functions
We show that all Feynman integrals in two Euclidean dimensions with massless propagators and arbitrary non-integer propagator powers can be expressed...
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Voros Coefficients for the Hypergeometric Differential Equations and Eynard–Orantin’s Topological Recursion: Part I—For the Weber Equation
We develop the theory of quantization of spectral curves via the topological recursion. We formulate a quantization scheme of spectral curves which...
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A New Level-Crossing Two-State Model Solvable in Terms of Hypergeometric Functions
AbstractWe present a new exactly integrable time-dependent constant-amplitude level-crossing two-state quantum model for which the detuning of the...
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Hypergeometric Functions
Focus of this chapter is the hypergeometric function 2 F 1(a, b;c;z) in the complex domain with complex function parameters. Corresponding...
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Charged dust in Einstein–Gauss–Bonnet models
We investigate the influence of the higher order curvature terms on the static configuration of a charged dust distribution in EGB gravity. The EGB...
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Eikonal Quasinormal Modes, Photon Sphere and Shadow of a Charged Black Hole in the 4D Einstein-Gauss-Bonnet Gravity
In this work, we investigate the relationship between the geometrical properties, the photon sphere, the shadow, and the eikonal quasinormal modes of...
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Hypergeometric series representations of Feynman integrals by GKZ hypergeometric systems
We show that almost all Feynman integrals as well as their coefficients in a Laurent series in dimensional regularization can be written in terms of...
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D-brane Masses at Special Fibres of Hypergeometric Families of Calabi–Yau Threefolds, Modular Forms, and Periods
We consider the fourteen families W of Calabi–Yau threefolds with one complex structure parameter and Picard–Fuchs equation of hypergeometric type,...
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Celestial conformal blocks of massless scalars and analytic continuation of the Appell function F1
In celestial conformal field theory (CCFT), the 4d massless scalars are represented by 2d conformal operators with conformal dimensions h =
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q-Derivatives of Multivariable q-Hypergeometric Function with Respect to Their Parameters
AbstractWe consider the q-derivatives of the Srivastava and Daoust basic multivariable hypergeometric function with respect to the parameters. This...
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Implicit quiescent optical solitons for the concatenation model with nonlinear chromatic dispersion and in absence of self-phase modulation by lie symmetry
This paper delves into the recovery and analysis of stable and localized optical waveforms (solitons) within a concatenated optical system...
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A novel algorithm for nested summation and hypergeometric expansions
We consider a class of sums over products of Z -sums whose arguments differ by a symbolic integer. Such sums appear, for instance, in the expansion of...
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Introduction of Hypergeometric Function
In the previous two chapters, two important classes of special functions, Bessel functions and Legendre functions with the Legendre polynomials as a...
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Series Representations for the Characteristic Function of the Multidimensional Markov Random Flight
We consider the symmetric Markov random flight, also called the persistent random walk, performed by a particle that moves at constant finite speed...
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Arithmetic Properties of Generalized Hypergeometric F-Series
In the paper, using a generalization of the Siegel-Shidlovskii method in the theory of transcendental numbers, we prove the infinite algebraic...
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The Virasoro fusion kernel and Ruijsenaars’ hypergeometric function
We show that the Virasoro fusion kernel is equal to Ruijsenaars’ hypergeometric function up to normalization. More precisely, we prove that the...
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Accessible soliton solutions with initial phase-front curvature in strongly nonlocal nonlinear media
Based on the extended fractional dimensional nonlinear Schrödinger equation and the variable separation method, a fractional accessible soliton...
