Borel transform theory

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21: Bibliography Z

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The Dilogarithm Function in Geometry and Number Theory. In Number Theory and Related Topics (Bombay, 1988), R. Askey and others (Eds.), Tata Inst. Fund. Res. Stud. Math., Vol. 12, pp. 231–249.

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MathReview (J. Browkin), ZentralBlatt

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§25.12(i).

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Distribution Theory and Transform Analysis, An Introduction and Generalized Functions with Applications. Dover, New York.

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Notes:

Reprint of 1965 McGraw-Hill Publication

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ISBN 0-486-65479-6, MathReview Entry

Referenced by:

§1.16(ix).

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On some classes of polynomials orthogonal on arcs of the unit circle connected with symmetric orthogonal polynomials on an interval. J. Approx. Theory 94 (1), pp. 73–106.

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ISSN 0021-9045, Link, MathReview (T. S. Chihara), ZentralBlatt

Referenced by:

§18.33(iii).

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Generalized Watson Transforms and Applications to Group Representations. Ph.D. Thesis, University of Vermont, Burlington,VT.

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§35.7(ii).

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A fast Fourier-Bessel transform algorithm. Zh. Vychisl. Mat. i Mat. Fiz. 35 (7), pp. 1128–1133 (Russian).

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Notes:

English translation in Comput. Math. Math. Phys. 35(7), pp. 901–905

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ISSN 0044-4669, MathReview (Vítĕzslav Veselý), ZentralBlatt

Referenced by:

§10.74(vii).

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22: Bibliography F

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Theory and Computation of Spheroidal Harmonics with General Arguments. Master’s Thesis, The University of Western Australia, Department of Physics.

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Notes:

Contains Mathematica package for spheroidal wave functions of complex arguments with complex parameters.

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FullText

Referenced by:

§30.12, 1st item, 2nd item.

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Un théorème de Paley-Wiener pour la transformation de Fourier sur un espace riemannien symétrique de rang un. J. Funct. Anal. 49 (2), pp. 230–268.

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ISSN 0022-1236, Document, Link, MathReview (Mogens Flensted-Jensen), ZentralBlatt

Referenced by:

§18.39(i).

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Application of the $\tau$-function theory of Painlevé equations to random matrices: PIV, PII and the GUE. Comm. Math. Phys. 219 (2), pp. 357–398.

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ISSN 0010-3616, Document, MathReview (Alexei Khorunzhy), ZentralBlatt

Referenced by:

§32.10(iv), §32.14, §32.6(v).

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On the asymptotic expansion of Mellin transforms. SIAM J. Math. Anal. 18 (1), pp. 273–282.

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ISSN 0036-1410, Document, Link, MathReview (Archibald Brown), ZentralBlatt

Referenced by:

§2.3(vi).

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Introduction to the Random Matrix Theory: Gaussian Unitary Ensemble and Beyond. In Recent Perspectives in Random Matrix Theory and Number Theory, London Math. Soc. Lecture Note Ser., Vol. 322, pp. 31–78.

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MathReview, ZentralBlatt

Referenced by:

§18.38(ii).

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23: Bille C. Carlson

… ►The main theme of Carlson’s mathematical research has been to expose previously hidden permutation symmetries that can eliminate a set of transformations and thereby replace many formulas by a few. …This symmetry led to the development of symmetric elliptic integrals, which are free from the transformations of modulus and amplitude that complicate the Legendre theory. …

24: Bibliography J

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Fast Hankel transforms. Geophysical Prospecting 27 (4), pp. 876–901.

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Document

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§10.74(vii).

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Atomic Structure Theory: Lectures on Atomic Physics. Springer, Berlin and Heidelberg.

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ISBN 978-3-540-68010-9

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§33.22(iv).

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The Theory of Electromagnetism. International Series of Monographs on Pure and Applied Mathematics, Vol. 47. A Pergamon Press Book, The Macmillan Co., New York.

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MathReview (W. E. Williams), ZentralBlatt

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§23.21(iii).

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Asymptotic behavior of the continued fraction coefficients of a class of Stieltjes transforms including the Binet function. In Orthogonal functions, moment theory, and continued fractions (Campinas, 1996), Lecture Notes in Pure and Appl. Math., Vol. 199, pp. 257–274.

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MathReview (Olav Njåstad), ZentralBlatt

Referenced by:

§5.10, §5.10.

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Angular Momentum Theory for Diatomic Molecules. Academic Press, New York.

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ISBN 0-12-391950-9

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§30.12, §34.12, Profile Brian R. Judd.

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25: Bibliography V

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An integral transform involving Heun functions and a related eigenvalue problem. SIAM J. Math. Anal. 17 (3), pp. 688–703.

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ISSN 0036-1410, Document, MathReview (William L. Perry), ZentralBlatt

Referenced by:

§31.10(i).

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Quantum Theory of Angular Momentum. World Scientific Publishing Co. Inc., Singapore.

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ISBN 9971-50-107-4, MathReview (M. A. Rashid), ZentralBlatt

Referenced by:

§16.24(iii), §34.1, §34.11, §34.13, §34.13, §34.14, §34.2, §34.3(iii), §34.3(vi), §34.4, §34.4, §34.5(iii), §34.5(vi), §34.7(ii), §34.7(iii), §34.8, §34.9, Ch.34.

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Transformations of some Gauss hypergeometric functions. J. Comput. Appl. Math. 178 (1-2), pp. 473–487.

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ISSN 0377-0427, Document, Link, MathReview (Wolfgang Bühring), ZentralBlatt

Referenced by:

§15.8(v).

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Special Functions and the Theory of Group Representations. American Mathematical Society, Providence, RI.

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MathReview, ZentralBlatt

Referenced by:

§13.27.

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The topological degree theory for the localization and computation of complex zeros of Bessel functions. Numer. Funct. Anal. Optim. 18 (1-2), pp. 227–234.

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ISSN 0163-0563, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vi).

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26: Bibliography P

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Statistical Field Theory. Addison-Wesley, Reading, MA.

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ISBN 0-201-05985-1, MathReview (Tony C. Dorlas), ZentralBlatt

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§22.19(ii).

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La Théorie des Fonctions de Bessel Exposée en vue de ses Applications à la Physique Mathématique. Centre National de la Recherche Scientifique, Paris (French).

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MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§10.63(ii).

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Gauge Field Theories. Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.

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ISBN 0-521-26537-1, MathReview (G. R. Allcock), ZentralBlatt

Referenced by:

§22.19(ii).

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String Theory: An Introduction to the Bosonic String, Vol. I. Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.

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ISBN 0-521-63303-6, MathReview (Angel Maria Uranga), ZentralBlatt

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3rd item.

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Catastrophe Theory and its Applications. Pitman, London.

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Notes:

Reprinted by Dover in 1996.

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ISBN 0-273-01029-8, MathReview (George K. Francis), ZentralBlatt

Referenced by:

§36.4(i), Ch.36.

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27: 2.6 Distributional Methods

… ►For an introduction to distribution theory, see Wong (1989, Chapter 5). … ►

§2.6(ii) Stieltjes Transform

… ►The Stieltjes transform of $f(t)$ is defined by … ►Corresponding results for the generalized Stieltjes transform … ►where $ℳf\left(z\right)$ is the Mellin transform of $f$ or its analytic continuation. …

28: Bibliography L

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The Classical Theory of Fields. Pergamon Press, Oxford.

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Notes:

Revised second edition. Course of Theoretical Physics, Vol. 2. Translated from the Russian by Morton Hamermesh

External Links:

MathReview (E. L. Hill), ZentralBlatt

Referenced by:

§9.16.

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Quantum Mechanics: Non-relativistic Theory. Pergamon Press Ltd., Oxford.

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Notes:

Revised second edition. Course of Theoretical Physics, Vol. 3. Translated from the Russian by J. B. Sykes and J. S. Bell

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MathReview, ZentralBlatt

Referenced by:

§9.16.

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Essai sur la Théorie des Nombres. 2nd edition, Courcier, Paris.

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ZentralBlatt

Referenced by:

§27.2(i).

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Zur Theorie der Gaußschen Summen. Math. Ann. 57 (4), pp. 554–567 (German).

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ISSN 0025-5831, Document, MathReview Entry, ZentralBlatt

Referenced by:

§20.11(i).

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Kinetic Theory: Classical, Quantum, and Relativistic Descriptions. third edition, Springer, New York.

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ISBN 0387955518

Referenced by:

§18.39(iii).

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29: 10.74 Methods of Computation

… ►And since there are no error terms they could, in theory, be used for all values of $z$; however, there may be severe cancellation when $|z|$ is not large compared with $n^2$. … ►

Hankel Transform

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Spherical Bessel Transform

►The spherical Bessel transform is the Hankel transform (10.22.76) in the case when $\nu$ is half an odd positive integer. … ►

Kontorovich–Lebedev Transform

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30: 6.17 Physical Applications

§6.17 Physical Applications

►Geller and Ng (1969) cites work with applications from diffusion theory, transport problems, the study of the radiative equilibrium of stellar atmospheres, and the evaluation of exchange integrals occurring in quantum mechanics. …Lebedev (1965) gives an application to electromagnetic theory (radiation of a linear half-wave oscillator), in which sine and cosine integrals are used.