Analytic continuation of the Appell function \(F_1\) and integration of the associated system of equations in the logarithmic case

DOI10.1134/S0965542517040042zbMath1377.33010OpenAlexW2615988577MaRDI QIDQ1682901

S. I. Bezrodnykh

Publication date: 6 December 2017

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542517040042

zbMATH Keywords

analytic continuationsystem of partial differential equationsBarnes-type integralshypergeometric functions two variables

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Appell, Horn and Lauricella functions (33C65)

Related Items (10)

Analytical solution for the cavitating flow over a wedge. I ⋮ Analytic continuation of Lauricella's function F_D^(N) for large in modulo variables near hyperplanes {z_j = z_l} ⋮ Convergent expansions and bounds for the incomplete elliptic integral of the second kind near the logarithmic singularity ⋮ Conformal mapping of a \(Z\)-shaped domain ⋮ Celestial conformal blocks of massless scalars and analytic continuation of the Appell function \(F_1\) ⋮ Analytic continuation of the Lauricella function with arbitrary number of variables ⋮ The Lauricella hypergeometric function $F_D^{(N)}$, the Riemann–Hilbert problem, and some applications ⋮ Using functional equations to calculate Feynman integrals ⋮ Analytic continuation of the Horn hypergeometric series with an arbitrary number of variables ⋮ Hypergeometric Functions and Feynman Diagrams

Uses Software

• SCPACK

Cites Work

• On the analytic continuation of the Lauricella function \(F_D^{(N)}\)
• Singular Riemann-Hilbert problem in complex-shaped domains
• Multipole method for the Dirichlet problem on doubly connected domains of complex geometry: A general description of the method
• Monodromy of hypergeometric functions and non-lattice integral monodromy
• The Riemann-Hilbert problem in a complicated domain for a model of magnetic reconnection in a plasma
• Generalized hypergeometric functions with applications in statistics and physical sciences
• Analytic continuation formulas and Jacobi-type relations for Lauricella function
• Hypergeometric functions of two variables
• Theory of Hypergeometric Functions
• Numerical Computation of the Schwarz–Christoffel Transformation
• Schwarz-Christoffel Mapping
• Singularities of hypergeometric functions in several variables
• Conformal mapping of rectangular heptagons
• Integration of the Partial Differential Equations for the Hypergeometric Functions F1 and FD of Two and More Variables
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