DISCRETE RICCATI EQUATION, HYPERGEOMETRIC FUNCTIONS AND CIRCLE PATTERNS OF SCHRAMM TYPE
Glasgow mathematical journal, Tome 47 (2005) no. A, pp. 1-16
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Square grid circle patterns with prescribed intersection angles, mimicking holomorphic maps $z^{\gamma }$ and ${\rm log}(z)$ are studied. It is shown that the corresponding circle patterns are embedded and described by special separatrix solutions of discrete Painlevé and Riccati equations. The general solution of this Riccati equation is expressed in terms of the hypergeometric function. Global properties of these solutions, as well as of the discrete $z^{\gamma }$ and ${\rm log}(z)$, are established.
AGAFONOV, S. I. DISCRETE RICCATI EQUATION, HYPERGEOMETRIC FUNCTIONS AND CIRCLE PATTERNS OF SCHRAMM TYPE. Glasgow mathematical journal, Tome 47 (2005) no. A, pp. 1-16. doi: 10.1017/S0017089505002247
@article{10_1017_S0017089505002247,
author = {AGAFONOV, S. I.},
title = {DISCRETE {RICCATI} {EQUATION,} {HYPERGEOMETRIC} {FUNCTIONS} {AND} {CIRCLE} {PATTERNS} {OF} {SCHRAMM} {TYPE}},
journal = {Glasgow mathematical journal},
pages = {1--16},
year = {2005},
volume = {47},
number = {A},
doi = {10.1017/S0017089505002247},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089505002247/}
}
TY - JOUR AU - AGAFONOV, S. I. TI - DISCRETE RICCATI EQUATION, HYPERGEOMETRIC FUNCTIONS AND CIRCLE PATTERNS OF SCHRAMM TYPE JO - Glasgow mathematical journal PY - 2005 SP - 1 EP - 16 VL - 47 IS - A UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089505002247/ DO - 10.1017/S0017089505002247 ID - 10_1017_S0017089505002247 ER -
%0 Journal Article %A AGAFONOV, S. I. %T DISCRETE RICCATI EQUATION, HYPERGEOMETRIC FUNCTIONS AND CIRCLE PATTERNS OF SCHRAMM TYPE %J Glasgow mathematical journal %D 2005 %P 1-16 %V 47 %N A %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089505002247/ %R 10.1017/S0017089505002247 %F 10_1017_S0017089505002247
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