On spectral asymptotic of quasi-exactly solvable quartic potential
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Bender, C., Boettcher, S.: Quasi-exactly solvable quartic potential. J. Phys. A 31(14), L273–L277 (1998)
Beraha, S., Kahane, J., Weiss, N.J.: Limits of zeros of recursively defined families of polynomials, in “Studies in Foundations and Combinatorics”, pp. 213–232, Advances in Mathematics Supplementary Studies Vol. 1, ed. G.-C. Rota, Academic Press, New York, (1978)
Bertola, M., Bothner, T.: Zeros of large degree Vorob’ev–Yablonski polynomials via a Hankel determinant identity. Int. Math. Res. Not. IMRN 19, 9330–9399 (2015)
Borcea, J., Bøgvad, R., Shapiro, B.: On rational approximation of algebraic functions. Adv. Math. 204(2), 448–480 (2006)
Borcea, J., Bøgvad, R., Shapiro, B.: Homogenized spectral pencils for exactly solvable operators: asymptotics of polynomial eigenfunctions. Publ. RIMS 45, 525–568 (2009)
Bøgvad, R., Shapiro, B.: On motherbody measures with algebraic Cauchy transform. Enseign. Math. 62(1–2), 117–142 (2016)
Bourget, A., McMillen, T.: On the distribution and interlacing of the zeros of Stieltjes polynomials. Proc. AMS 138, 3267–3275 (2010)
Bourget, A., McMillen, T., Vargas, A.: Interlacing and nonorthogonality of spectral polynomials for the Lamé operator. Proc. AMS 137, 1699–1710 (2009)
Buckingham, R.J., Miller, P.D.: Large-degree asymptotics of rational Painlevé II functions: noncritical behaviour. Nonlinearity 27(10), 2489–2578 (2014)
Buckingham, R.J., Miller, P.D.: Large-degree asymptotics of rational Painlevé II functions: critical behaviour. Nonlinearity 28(6), 1539–1596 (2015)
Clarkson, P.A., Mansfield, E.L.: The second Painlevé equation, its hierarchy and associated special polynomials. Nonlinearity 16, R1–R26 (2003)
Coussement, E., Coussement, J., Van Assche, W.: Asymptotic zero distribution for a class of multiple orthogonal polynomials. Trans. Am. Math. Soc. 360, 5571–5588 (2008)
Eremenko, A., Gabrielov, A.: Quasi-exactly solvable quartic: elementary integrals and asymptotics. J. Phys. A Math. Theor. 44, 312001 (2011)
Fisk, S.: Polynomials, roots, and interlacing, arXiv:math/0612833
Kametaka, Y.: On poles of the rational solution of the toda equation of Painlevé-II Type, Proc. Japan Acad. Ser A, 59(A), 358–360 (1983)
Kuijlaars, A.B.J., Van Assche, W.: The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients. J. Approx. Theory 99, 167–197 (1999)
Masoero, D.: Poles of integrale tritronquée and anharmonic oscillators. A WKB approach. J. Phys. A: Math. Theor. 43(9), 5201 (2010)
Masoero, D., De Benedetti, V.: Poles of integrale tritronquée and anharmonic oscillators. Asymptotic localization from WKB analysis. Nonlinearity 23, 2501 (2010)
Mukhin, E., Tarasov, V.: On conjectures of A. Eremenko and A. Gabrielov for quasi-exactly solvable quartic. Lett. Math. Phys. 103(6), 653–663 (2013)
Nilsson, N.: Some growth and ramification properties of certain integrals on algebraic manifold. Ark. Mat. 5(1965), 463–476 (1965)
Petkovšek, M., Zakrajšek, H.: Pascal-like determinants are recursive. Adv. Appl. Math. 33, 431–450 (2004)
Shapiro, B., Tater, M.: Asymptotics of spectral polynomials. Acta Polytechnica 47(2–3), 32–35 (2007)
Shapiro, B., Tater, M.: On spectral polynomials of the Heun equation. I, JAT 162, 766–781 (2010)
Shin, K.: Eigenvalues of PT-symmetric oscillators with polynomial potentials. J. Phys. A 38(27), 6147–6166 (2005)
Strebel, K.: Quadratic differentials, Ergebnisse der Mathematik und ihrer Grenzgebiete, 5, Springer-Verlag, Berlin, (1984), xii+184 pp
Shapiro, B., Takemura, K., Tater, M.: On spectral polynomials of the Heun equation II. Commun. Math. Phys. 311(2), 277–300 (2012)
Taneda, M.: Remarks on the Yablonskii–Vorob’ev polynomials. Nagoya Math. J. 159, 87–111 (2000)
Vorob’ev, A.: On rational solutions of the second Painlevé equations, Diff. Eqns (1) (1965), 58–59 (in Russian)
Yablonskii, A.: On rational solutions of the second Painlevé equation, Vesti Akad. Navuk. BSSR Ser. Fiz. Tkh. Nauk. 3, 30–35 (1959). ((in Russian))