Borel transform theory
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31—40 of 258 matching pages
31: Bibliography G
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Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics.
Developments in Mathematics, Vol. 4, Kluwer Academic Publishers, Dordrecht.
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WKB and turning point theory for second-order difference equations.
In Spectral Methods for Operators of Mathematical Physics,
Oper. Theory Adv. Appl., Vol. 154, pp. 101–138.
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Numerical Analysis of Spectral Methods: Theory and Applications.
Society for Industrial and Applied Mathematics, Philadelphia, PA.
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Linear Differential Equations and Group Theory from Riemann to Poincaré.
2nd edition, Birkhäuser Boston Inc., Boston, MA.
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Kinetic theory of linear shear flow.
Phys. Fluids 1 (3), pp. 215–224.
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32: Bibliography D
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Multiplicative Number Theory.
3rd edition, Graduate Texts in Mathematics, Vol. 74, Springer-Verlag, New York.
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Pólya’s Theory of Counting.
In Applied Combinatorial Mathematics, E. F. Beckenbach (Ed.),
pp. 144–184.
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Elements of the Theory of Numbers.
Harcourt/Academic Press, San Diego, CA.
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History of the Theory of Numbers (3 volumes).
Carnegie Institution of Washington, Washington, D.C..
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Handbuch der Laplace-Transformation. Bd. II. Anwendungen der Laplace-Transformation. 1. Abteilung.
Birkhäuser Verlag, Basel und Stuttgart (German).
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33: Bibliography E
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The numerical inversion of two classes of Kontorovich-Lebedev transform by direct quadrature.
J. Comput. Appl. Math. 61 (1), pp. 43–72.
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Tables of Integral Transforms. Vol. II.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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On the transformation theory of ordinary second-order linear symmetric differential expressions.
Czechoslovak Math. J. 32(107) (2), pp. 275–306.
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A catalogue of Sturm-Liouville differential equations.
In Sturm-Liouville theory,
pp. 271–331.
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Charles Sturm and the development of Sturm-Liouville theory in the years 1900 to 1950.
In Sturm-Liouville theory,
pp. 45–74.
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34: Bibliography C
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Introduction to the Theory of Fourier’s Series and Integrals.
3rd edition, Macmillan, London.
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The Mathematical Theory of Black Holes.
In General Relativity and Gravitation (Padova, 1983),
pp. 5–26.
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Introduction to Approximation Theory.
2nd edition, Chelsea Publishing Co., New York.
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Theory of ordinary differential equations.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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A Course in Computational Algebraic Number Theory.
Springer-Verlag, Berlin-New York.
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35: Bibliography R
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Topics in Analytic Number Theory.
Springer-Verlag, New York.
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Methods of Modern Mathematical Physics, Vol. 3, Scattering Theory.
Academic Press, New York.
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Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse.
Inauguraldissertation, Göttingen.
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Elementary Number Theory and its Applications.
5th edition, Addison-Wesley, Reading, MA.
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On the foundations of combinatorial theory. I. Theory of Möbius functions.
Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2, pp. 340–368.
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36: Bibliography K
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Replica field theories, Painlevé transcendents, and exact correlation functions.
Phys. Rev. Lett. 89 (25), pp. (250201–1)–(250201–4).
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Neue Untersuchungen einer Reihe aus der Theorie der elliptischen Funktionen.
Journal für die Reine und Angenwandte Mathematik 158, pp. 209–218 (German).
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Theorie und Anwendung der unendlichen Reihen.
4th edition, Die Grundlehren der mathematischen Wissenschaften, Band 2, Springer-Verlag, Berlin-Heidelberg (German).
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Zur Theorie der Modulformen -ten Grades. I.
Math. Z. 59, pp. 399–416 (German).
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A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transformation.
Mir, Moscow.
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37: Bibliography H
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Quantum theory for mathematicians.
Graduate Texts in Mathematics, Vol. 267, Springer, New York.
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Fast Hankel transform algorithm.
IEEE Trans. Acoust. Speech Signal Process. 32 (3), pp. 666–671.
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An Introduction to the Theory of Numbers.
5th edition, The Clarendon Press Oxford University Press, New York-Oxford.
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Molecular Electronic-Structure Theory.
John Wiley & Sons, New York.
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The Theory of Spherical and Ellipsoidal Harmonics.
Cambridge University Press, London-New York.
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38: 21.9 Integrable Equations
§21.9 Integrable Equations
►Riemann theta functions arise in the study of integrable differential equations that have applications in many areas, including fluid mechanics (Ablowitz and Segur (1981, Chapter 4)), magnetic monopoles (Ercolani and Sinha (1989)), and string theory (Deligne et al. (1999, Part 3)). … ►All quantities are made dimensionless by a suitable scaling transformation. …39: 20.14 Methods of Computation
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►For values of near the transformations of §20.7(viii) can be used to replace with a value that has a larger imaginary part and hence a smaller value of .
…In theory, starting from any value of , a finite number of applications of the transformations
and will result in a value of with ; see §23.18.
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