Geodesic
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 
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/
@article{ZNSL_2014_426_a4,
     author = {A. Ya. Kazakov},
     title = {Integral symmetry for the confluent {Heun} equation with added apparent singularity},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {34--48},
     year = {2014},
     volume = {426},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_426_a4/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[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