Integral symmetry for the confluent Heun equation with added apparent singularity
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 44, Tome 426 (2014), pp. 34-48 Cet article a éte moissonné depuis la source Math-Net.Ru

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Confluent Heun equation with added apparent singular point is under consideration. New integral transform connecting solutions of this equation with different parameters is obtained. Kernel of this transform is a suitable solution of the confluent hypergeometric equation.
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A. Ya. Kazakov. Integral symmetry for the confluent Heun equation with added apparent singularity. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 44, Tome 426 (2014), pp. 34-48. http://geodesic.mathdoc.fr/item/ZNSL_2014_426_a4/

[1] H. Bateman, A. Erdelyi, Higher transcendental functions, v. 1, McCraw-Hill Book Company Inc., New York, 1953 | MR

[2] M. Abramowitz, I. A. Stegun, Handbook of mathematical functions, National Bureau of Standards, 1964

[3] W. Vasov, Asymptotic expansions for ordinary differential equations, John Wiley, New York, 1965

[4] A. A. Bolibrukh, Fuchsian differential equations and holomorphic bundles, MCCME, Moscow, 2000

[5] Y. Sibuya, Linear ODE in complex domain, Analytic continuation, AMS, Providence, Rhode Island, 1990

[6] K. Iwasaki, H. Kimura, S. Shimomura, M. Yosida, From Gauss to Painleve: A modern theory of special functions, Vieweg, Braunshweig, 1991 | MR | Zbl

[7] S. Yu. Slavyanov, W. Lay, Special functions: A unified theory based on singularities, Oxford university press, Oxford–New York, 2000 | MR | Zbl

[8] A. Ya. Kazakov, “Euler integral symmetry and deformed hypergeometric equation”, J. Math. Sci., 185:4 (2012), 573–580 | DOI | MR | Zbl

[9] A. Ya. Kazakov, “Monodromy of Heun equations with apparent singularities”, Intern. J. Theor. Math. Phys., 3:6 (2013), 190–196

[10] A. V. Shanin, R. V. Craster, “Removing false singular points as a method of solving ordinary differential equations”, Euro. J. Appl. Math., 13 (2002), 617–639 | DOI | MR | Zbl

[11] A. Ishkhanyan, K. A. Suominen, “New solutions of Heun's general equation”, J. Phys. A, 36 (2003), L81–L85 | DOI | MR | Zbl

[12] A. Ya. Kazakov, “Integral symmetry, integral invariants and monodromy of ordinary differential equations”, Theor. Math. Phys., 116:3 (1998), 991–1000 | DOI | MR | Zbl

[13] A. Ya. Kazakov, S. Yu. Slavyanov, “Integral relations for the special functions of the Heun class”, Theor. Math. Phys., 107:3 (1996), 388–396 | DOI | MR | Zbl

[14] L. J. El-Jaick, B. D. B. Figueiredo, “Transformation of Heun equation and its integral relations”, J. Phys. A, 44 (2011), 075204 | DOI | MR | Zbl

[15] A. Ya. Kazakov, S. Yu. Slavyanov, “Euler integral symmetries for a deformed Heun equation and symmetries of the Painleve PVI equation”, Theor. Math. Phys., 155:2 (2008), 722–733 | DOI | MR | Zbl

[16] K. Takemura, “Middle convolution and Heun's equation”, SIGMA, 5 (2009), 040, 22 pp. | DOI | MR | Zbl

[17] M. Detweiler, S. Reiter, “Middle convolution of Fuchsian systems and the construction of rigid differential systems”, J. Algebra, 318 (2007), 1–24 | DOI | MR

[18] A. Ya. Kazakov, S. Yu. Slavyanov, “Euler integral symmetries for a deformed confluent Heun equation and symmetries of the Painleve PV equation”, Theor. Math. Phys., 179:2 (2014), 543–549 | DOI

[19] A. Ya. Kazakov, “Symmetries of the confluent Heun equation”, J. Math. Sci., 117:2 (2003), 3918–3927 | DOI | MR | Zbl

[20] A. Ya. Kazakov, “Isomonodromy deformation of the Heun class equation”, Painleve Equations and related topics, De Gruyter Proceedings in mathematics, eds. A. D. Bruno, A. B. Batkhin, 2012, 107–116 | MR | Zbl

[21] A. Castro, J. M. Lapan, A. Maloney, M. J. Rodriguez, “Black hole scattering from monodromy”, Class. Quant. Gravity, 30 (2013), 165005 | DOI | MR | Zbl

[22] I. S. Gradshteyn, I. M. Ryzhik, Table of integrals, series and products, Academic Press Inc., 1994 | MR | Zbl