An entire function defined by a nonlinear recurrence relation

Journal of the London Mathematical Society

Volumn 66, Issue 2, 2002, Pages 377-387

  Hone, A N W ^a,b   Joshi, N ^a,c   Kitaev, A V ^a,d  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b UNIVERSITY OF KENT   (United Kingdom)

^c UNIVERSITY OF SYDNEY   (Australia)

^d STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036807120     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024610702003423     Document Type: Article

References (7)

1. M. Abramowitz and I. Stegun, Handbook of mathematical functions (Dover, New York, 1970).
2. B. Eynard and J. Zinn-Justin, 'Large order behaviour of 2D gravity coupled to D < 1 matter' Phys. Lett. B 302 (1993) 396-402.
3. N. Joshi and A.V. Kitaev, On Boutroux's tritronquée solutions of the first Painlevé equation, Studies in Applied Mathematics 107 (Elsevier, 2001) 253-291.
4. M.D. Kruskal, N. Joshi and R. Halburd, 'Analytic and asymptotic methods for nonlinear singularity analysis: a review and extensions of tests for the Painlevé property', Proceedings of CIMPA Summer School on Nonlinear Systems, Lecture Notes in Physics 495 (ed. B. Grammaticos and K. Tamizhmani, Springer, Heidelberg, 1997) 171-205.
5. Y. Takei, On the connection formula for the first Painlevé equation from the viewpoint of the exact WKB analysis. Painlevé functions and asymptotic analysis, Surikaisekikenkyusho Kokyuroku 931 (Kyoto University, 1995) 70-99 (Japanese).
6. A. Tovbis, 'On exponentially small terms of solutions to nonlinear ordinary differential equations', Methods Appl. Anal. 1 (1994) 57-74.
7. A. Tovbis, 'Nonlinear differential equations resolvable with respect to an irregular singular point', J. Differential Equations 109 (1994) 201-224.