of Hill equation
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21—30 of 30 matching pages
21: Bibliography Z
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On the Computation of Zeros of Bessel and Bessel-related Functions.
In Proceedings of the Sixth International Colloquium on
Differential Equations (Plovdiv, Bulgaria, 1995), D. Bainov (Ed.),
Utrecht, pp. 409–416.
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Doron Zeilberger’s Maple Packages and Programs
Department of Mathematics, Rutgers University, New Jersey.
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Distribution Theory and Transform Analysis, An Introduction and Generalized Functions with Applications.
Dover, New York.
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Error bounds for asymptotic solutions of second-order linear difference equations.
J. Comput. Appl. Math. 71 (2), pp. 191–212.
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22: Bibliography E
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Tables of Integral Transforms. Vol. II.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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Integral equations for Heun functions.
Quart. J. Math., Oxford Ser. 13, pp. 107–112.
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The Fuchsian equation of second order with four singularities.
Duke Math. J. 9 (1), pp. 48–58.
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Higher Transcendental Functions. Vol. III.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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A catalogue of Sturm-Liouville differential equations.
In Sturm-Liouville theory,
pp. 271–331.
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23: Bibliography V
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A Mathieu equation for ships rolling among waves. I, II.
Norske Vid. Selsk. Forh., Trondheim 22 (25–26), pp. 113–123.
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Integralgleichungen für periodische Lösungen Hill’scher Differentialgleichungen.
Analysis 3 (1-4), pp. 189–203 (German).
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On the growth of convergence radii for the eigenvalues of the Mathieu equation.
Math. Nachr. 192, pp. 239–253.
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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
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On the rational solutions of the second Painlevé equation.
Differ. Uravn. 1 (1), pp. 79–81 (Russian).
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24: Bibliography I
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Ordinary Differential Equations.
Longmans, Green and Co., London.
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A First Course in the Numerical Analysis of Differential Equations.
Cambridge Texts in Applied Mathematics, No. 15, Cambridge University Press, Cambridge.
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On the asymptotic analysis of the Painlevé equations via the isomonodromy method.
Nonlinearity 7 (5), pp. 1291–1325.
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The Isomonodromic Deformation Method in the Theory of Painlevé Equations.
Lecture Notes in Mathematics, Vol. 1191, Springer-Verlag, Berlin.
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Quantum Field Theory.
International Series in Pure and Applied Physics, McGraw-Hill International Book Co., New York.
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25: Bibliography L
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Some differential equations and associated integral equations.
Quart. J. Math. (Oxford) 5, pp. 81–97.
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The Classical Theory of Fields.
Pergamon Press, Oxford.
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Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics.
J. Math. Phys. 27 (5), pp. 1238–1265.
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The second Painlevé equation.
Differ. Uravn. 7 (6), pp. 1124–1125 (Russian).
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Integrals of Bessel Functions.
McGraw-Hill Book Co., Inc., New York.
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26: Bibliography R
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Diffraction of plane radio waves by a parabolic cylinder. Calculation of shadows behind hills.
Bell System Tech. J. 33, pp. 417–504.
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Asymptotics and Bounds of the Roots of Equations (Russian).
Zinatne, Riga.
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Real and complex analysis.
McGraw-Hill Book Co., New York-Toronto, Ont.-London.
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Functional Analysis.
McGraw-Hill Book Co., New York.
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Principles of Mathematical Analysis.
3rd edition, McGraw-Hill Book Co., New York.
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27: Bibliography P
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Sur les équations différentielles du second ordre à points critiques fixès.
C.R. Acad. Sc. Paris 143, pp. 1111–1117.
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Signal Analysis.
McGraw-Hill, New York.
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Smoothing of the Stokes phenomenon for high-order differential equations.
Proc. Roy. Soc. London Ser. A 436, pp. 165–186.
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A uniform asymptotic expansion for the incomplete gamma function.
J. Comput. Appl. Math. 148 (2), pp. 323–339.
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Remarks on computing the probability integral in one and two dimensions.
In Proceedings of the Berkeley Symposium on Mathematical
Statistics and Probability, 1945, 1946,
pp. 63–78.
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28: 25.12 Polylogarithms
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►The notation was introduced in Lewin (1981) for a function discussed in Euler (1768) and called the dilogarithm in Hill (1828):
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►The remainder of the equations in this subsection apply to principal branches.
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29: Bibliography B
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Integral equations and exact solutions for the fourth Painlevé equation.
Proc. Roy. Soc. London Ser. A 437, pp. 1–24.
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An Introduction to Linear Difference Equations.
Dover Publications Inc., New York.
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Advanced Mathematical Methods for Scientists and Engineers.
McGraw-Hill Book Co., New York.
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Vortices in Ginzburg-Landau Equations.
In Proceedings of the International Congress of Mathematicians,
Vol. III (Berlin, 1998),
pp. 11–19.
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Ordinary differential equations.
Fourth edition, John Wiley & Sons, Inc., New York.
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30: Bibliography J
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Tafeln höherer Funktionen (Tables of Higher Functions).
7th edition, B. G. Teubner, Stuttgart (Bilingual).
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Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II.
Phys. D 2 (3), pp. 407–448.
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Differential equations and mathematical biology.
Chapman & Hall/CRC Mathematical and Computational Biology
Series, CRC Press, Boca Raton, FL.
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Differential equations and mathematical biology.
Chapman & Hall/CRC Mathematical Biology and Medicine Series, Chapman & Hall/CRC, Boca Raton, FL.
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On Boutroux’s tritronquée solutions of the first Painlevé equation.
Stud. Appl. Math. 107 (3), pp. 253–291.
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