Results 31 to 40 of about 3,218 (147)

Dirac-K\"ahler particle in Riemann spherical space: boson interpretation [PDF]

, 2014
In the context of the composite boson interpretation, we construct the exact general solution of the Dirac--K\"ahler equation for the case of the spherical Riemann space of constant positive curvature, for which due to the geometry itself one may expect ...
Florea, O., Ishkhanyan, A. M., Ovsiyuk, E. M., Red'kov, V. M.   +3 more
core   +1 more source

Derivatives of Horn hypergeometric functions with respect to their parameters

Journal of Mathematical Physics, 2017
The derivatives of eight Horn hypergeometric functions [four Appell F1, F2, F3, and F4, and four (degenerate) confluent Φ1, Φ2, Ψ1, and Ξ1] with respect to their parameters are studied. The first derivatives are expressed, systematically, as triple infinite summations or, alternatively, as single summations of two-variable Kampé de Fériet functions ...
Ancarani, L. U., del Punta, Jessica Adriana, Gasaneo, Gustavo   +2 more
openaire   +2 more sources

On convergence of branched continued fraction expansions of Horn's hypergeometric function $H_3$ ratios

Carpathian Mathematical Publications, 2021
The paper deals with the problem of convergence of the branched continued fractions with two branches of branching which are used to approximate the ratios of Horn's hypergeometric function $H_3(a,b;c;{\bf z})$. The case of real parameters $c\geq a\geq 0,$ $c\geq b\geq 0,$ $c\neq 0,$ and complex variable ${\bf z}=(z_1,z_2)$ is considered.
openaire   +3 more sources

Feynman integral in $\mathbb R^1\oplus\mathbb R^m$ and complex expansion of $_2F_1$

, 2016
Closed form expressions are proposed for the Feynman integral $$ I_{D, m}(p,q) = \int\frac{d^my}{(2\pi)^m}\int\frac{d^Dx}{(2\pi)^D} \frac1{(x-p/2)^2+(y-q/2)^4} \frac1{(x+p/2)^2+(y+q/2)^4} $$ over $d=D+m$ dimensional space with $(x,y),\,(p,q)\in
Pogány, Tibor K., Shpot, Mykola A.
core   +1 more source

Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

, 2009
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source.
A. Erdélyi, A.P. Prudnikov, D.H. Werner, G. Matviyenko, G.N. Watson, H.M. Srivastava, H.S. Cohl, H.S. Cohl, Howard S. Cohl, I.S. Gradshteyn, J. Mathews, J.T. Conway, J.T. Conway, John T. Conway, M. Abramowitz, P.L. Overfelt, P.M. Morse, P.R. Prentice, S. Wolfram   +18 more
core   +1 more source

Algebraicity of the Appell–Lauricella and Horn hypergeometric functions

Journal of Differential Equations, 2012
24 pages, 6 tables, 2 ...
openaire   +5 more sources

Recursion formulas for G1 and G2 horn hypergeometric functions

, 2020
The aim of this paper is to present various recursion formulas for Horn hypergeometric functions by the contiguous relations of hypergeometric series.These recursion formulas allow us to state the functions G1 and G2 Horn hypergeometric functions as a combination of themselves. © 2015 Miskolc University Press.
Sahin, Recep, Agha, Susan Ridha Shakor
openaire   +2 more sources

A new extended multivariable Horn function

International Journal of Mathematics for Industry
This study presents a new multivariable fourth class of Horn function. Additionally, for the new extended multivariable fourth-type Horn function, we create bilateral generating functions and particular generating functions for this multivariable fourth ...
Priyanka Gupta, Sunil Joshi, Ekta Mittal, Murli Manohar Gour   +3 more
doaj   +1 more source

Scalar one-loop vertex integrals as meromorphic functions of space-time dimension d [PDF]

, 2017
Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension $d$ in terms of (generalized) hypergeometric functions $_2F_1$ and $F_1$.
Bluemlein, Johannes, Phan, Khiem Hong, Riemann, Tord   +2 more
core   +2 more sources

On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function H4(a,b;c,d;z1,z2) Ratios

Axioms, 2023
The paper deals with the problem of representation of Horn’s hypergeometric functions by branched continued fractions. The formal branched continued fraction expansions for three different Horn’s hypergeometric function H4 ratios are constructed. The method employed is a two-dimensional generalization of the classical method of constructing of Gaussian
Tamara Antonova, Roman Dmytryshyn, Ilona-Anna Lutsiv, Serhii Sharyn   +3 more
openaire   +2 more sources