
This article is cited in 9 scientific papers (total in 9 papers)
Representations for Appell's series $F_2(x,y)$ to the vicinity of the singular point $(1,1)$ and near the boundary of its domain of convergence
V. F. Tarasov^{} ^{} Bryansk State Technical University
Abstract:
Exact analytical representations for Appell's series $F_2(x,y)$ to the vicinity of the singular point $(1,1)$ and the boundary of its domain of convergence are given. It is shown, that Appell's functions $F_2(1,1)$ and $F_3(1,1)$ have the property of mirrorlike symmetry with respect to the center $j_0=1/2$ under the change $j\mapstoj1$, $j\in\mathbb{Z}$, and they correlate between each other.
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517.588 Received: 01.04.1996
Citation:
V. F. Tarasov, “Representations for Appell's series $F_2(x,y)$ to the vicinity of the singular point $(1,1)$ and near the boundary of its domain of convergence”, Fundam. Prikl. Mat., 4:2 (1998), 669–689
Citation in format AMSBIB
\Bibitem{Tar98}
\by V.~F.~Tarasov
\paper Representations for Appell's series $F_2(x,y)$ to the vicinity of the singular point $(1,1)$ and near the boundary of its domain of convergence
\jour Fundam. Prikl. Mat.
\yr 1998
\vol 4
\issue 2
\pages 669689
\mathnet{http://mi.mathnet.ru/fpm326}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=1801181}
\zmath{https://zbmath.org/?q=an:0976.33010}
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This publication is cited in the following articles:

Tarasov V.F., “W. Gordon's integral (1929) and its representations by means of Appellis functions F2, F1 and F3”, Modern Physics Letters B, 16:23–24 (2002), 895–899

Tarasov V.F., “W. Gordon's integral (1929) and its representations by means of Appell's functions F2, F1, and F3”, Journal of Mathematical Physics, 44:3 (2003), 1449–1452

Tarasov V.F., “The ThomasFermigombas atom models in which the electrons are grouped into n and nlshells and a calculation of the atomic form factor”, International Journal of Modern Physics B, 18:3 (2004), 409–419

Tarasov V.F., “The HeunSchrodinger radial equation for DHatoms”, Modern Physics Letters B, 19:19–20 (2005), 981–989

Shpot M.A., “A massive Feynman integral and some reduction relations for Appell functions”, Journal of Mathematical Physics, 48:12 (2007), 123512

Tarasov V.F., “Exact analytical expressions and numerical values of diagonal matrix elements {$\langle r^k\rangle_{nlj}, \langle g\vert r^k\vert g\rangle, \langle g\vert r^k\vert f\rangle$} and {$\langle f\vert r^k\vert f\rangle$} with {D}irac's radial functions {$g(r)$} and {$f(r)$} of {H}like atoms and the symmetry of {A}ppell's function {$F_2(1,1)$}”, International Journal of Modern Physics B, 22:29 (2008), 5175–5205

Tarasov V.F., “Multipole matrix elements $\langle nlr^{\beta} n' l' \rangle_{\nu}$ for Hlike atoms, their asymptotics and applications $(AS \beta = 1, n \leq 4, n' \leq 10)$”, International Journal of Modern Physics B, 23:8 (2009), 2041–2067

Tarasov V.F., “Exact analytical expressions and numerical values of Slater's and Marvin's radial integrals of the type $R_k^{(\mu, \nu)} (11,21;12,22), F_k^{(\mu, \nu)} (1,2)$ and $G_k^{(\mu, \nu)} (1;2)$ with the kernel $r_<^{k+\mu}/r_>^{k+\mu}$ (as $k \geq 0, \mu \geq 0$ is an even and $\nu  \mu = 1,3,5, …$) for arbitrary $nl$states of Hlike atoms and $Z \leq 137$ by means of Appell's $F_2 (x,y)$ and Gauss's $_2F_1 (z)$ functions”, Internat J Modern Phys B, 24:27 (2010), 5387–5407

Tarasov V.F., “New properties of the {P}. {E}. {A}ppell hypergeometric series {$F_2(\alpha;\beta,\beta';\gamma,\gamma';x,y)$} to the vicinity of the singular point {$(1,1)$} and near the boundary of its domain of convergence {$D_2\colon\vert x\vert +\vert y\vert <1$}”, Internat J Modern Phys B, 24:22 (2010), 4181–4202

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