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1: 1.14 Integral Transforms

§1.14 Integral Transforms

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§1.14(i) Fourier Transform

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§1.14(iii) Laplace Transform

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Fourier Transform

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Laplace Transform

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2: Bibliography X

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Prolate spheroidal wavefunctions, quadrature and interpolation. Inverse Problems 17 (4), pp. 805–838.

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Notes:

Special issue to celebrate Pierre Sabatier’s 65th birthday (Montpellier, 2000)

External Links:

ISSN 0266-5611, Document, MathReview (Thomas Sauer), ZentralBlatt

Referenced by:

§30.13(v).

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3: Bibliography

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Exact linearization of a Painlevé transcendent. Phys. Rev. Lett. 38 (20), pp. 1103–1106.

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External Links:

Document, MathReview (Mark Adler)

Referenced by:

§32.11(ii), §32.13(i), §32.13(ii), §32.13(iii), §32.5.

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On the degrees of irreducible factors of higher order Bernoulli polynomials. Acta Arith. 62 (4), pp. 329–342.

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External Links:

ISSN 0065-1036, Pdf, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.12(iii).

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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics. Comput. Phys. Comm. 150 (1), pp. 1–20.

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Notes:

Includes algorithms for Lerch’s transcendent. C and Mathematica codes by Aksenov and Jentschura are available.

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Code, Document

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1st item.

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Catastrophe Theory. 2nd edition, Springer-Verlag, Berlin.

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Notes:

Translated from the Russian by G. S. Wassermann, based on a translation by R. K. Thomas. See also Arnol’d (1992).

External Links:

ISBN 3-540-16199-6, MathReview (James Callahan), ZentralBlatt

Referenced by:

Ch.36.

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Catastrophe Theory. 3rd edition, Springer-Verlag, Berlin.

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Notes:

Translated from the Russian by G. S. Wassermann, Based on a translation by R. K. Thomas

External Links:

ISBN 3-540-54811-4, MathReview (Peter Giblin), ZentralBlatt

Referenced by:

V. I. Arnol’d (1986).

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4: 35.8 Generalized Hypergeometric Functions of Matrix Argument

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Kummer Transformation

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Thomae Transformation

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Laplace Transform

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5: Bibliography S

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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean. SIAM J. Math. Anal. 20 (6), pp. 1514–1528.

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External Links:

ISSN 0036-1410, Document, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§22.19(i), §22.20(vi).

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Numerical evaluation of spherical Bessel transforms via fast Fourier transforms. J. Comput. Phys. 100 (2), pp. 294–296.

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External Links:

ISSN 0021-9991, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vii).

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Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.

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External Links:

Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§28.8(iv).

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Practical Extrapolation Methods: Theory and Applications. Cambridge Monographs on Applied and Computational Mathematics, Vol. 10, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-66159-5, MathReview (Thomas A. Atchison), ZentralBlatt

Referenced by:

§3.9(vi).

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A Maple package for symmetric functions. J. Symbolic Comput. 20 (5-6), pp. 755–768.

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Notes:

For software see John Stembridge’s home page. The SF package contains Maple software for zonal, Jack, and Macdonald polynomials.

External Links:

Home Page, ISSN 0747-7171, Document, MathReview, ZentralBlatt

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3rd item.

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6: Bibliography G

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Contiguous relations and summation and transformation formulae for basic hypergeometric series. J. Difference Equ. Appl. 19 (12), pp. 2029–2042.

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External Links:

ISSN 1023-6198, Document, FullText, MathReview (Thomas Britz), ZentralBlatt

Referenced by:

§17.7(iii).

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Problem 72-21, Laplace transforms of Airy functions. SIAM Rev. 15 (4), pp. 796–798.

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Notes:

Problem proposed by P. Smith.

External Links:

Document

Referenced by:

(9.10.14), (9.10.15), (9.10.16), §9.10(v).

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Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

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Notes:

Includes Fortran program claiming 12S accuracy

External Links:

ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt

Referenced by:

3rd item, §10.77(ix).

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Mutual integrability, quadratic algebras, and dynamical symmetry. Ann. Phys. 217 (1), pp. 1–20.

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External Links:

ISSN 0003-4916, Link, MathReview (A. O. Barut), ZentralBlatt

Referenced by:

§18.38(iii).

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Fourier transforms related to a root system of rank 1. Transform. Groups 12 (1), pp. 77–116.

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External Links:

ISSN 1083-4362, Link, MathReview (Genkai Zhang), ZentralBlatt

Referenced by:

§18.28(xi), §18.38(iii).

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7: Bibliography D

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Integral Transforms and their Applications. 2nd edition, Applied Mathematical Sciences, Vol. 25, Springer-Verlag, New York.

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External Links:

ISBN 0-387-96080-5, MathReview, ZentralBlatt

Referenced by:

§1.14(vii).

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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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External Links:

MathReview (I. I. Hirschman), ZentralBlatt

Referenced by:

§2.5(i).

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Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.

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Notes:

For a numerical error in one of the zeros see Amos (1985).

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

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2nd item.

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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.

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Notes:

(This reference has several typographical errors.)

External Links:

ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§13.21(ii), §13.21(iii), §13.21(iv).

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Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point. Anal. Appl. (Singap.) 12 (4), pp. 385–402.

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External Links:

ISSN 0219-5305, Document, Link, MathReview (Thomas Mbah Acho), ZentralBlatt

Referenced by:

5th item, §14.32.

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8: Bibliography B

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Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

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External Links:

Document

Referenced by:

§33.22(iv).

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A program for computing the Riemann zeta function for complex argument. Comput. Phys. Comm. 20 (3), pp. 441–445.

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Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

Document, Code, ZentralBlatt

Referenced by:

1st item.

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Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

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Notes:

Double-precision Fortran code.

External Links:

Document, Code

Referenced by:

1st item, 4th item.

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Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.

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External Links:

Document, ZentralBlatt

Referenced by:

§10.73(iv).

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Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model. Ann. of Math. (2) 150 (1), pp. 185–266.

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External Links:

ISSN 0003-486X, Document, MathReview (Thomas Kriecherbauer), ZentralBlatt

Referenced by:

§18.32.

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9: 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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External Links:

ISSN 0377-0427, Document, MathReview (J. P. Singhal), ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

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Tables of Integral Transforms. Vol. I. McGraw-Hill Book Company, Inc., New York-Toronto-London.

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Notes:

Table errata: Math. Comp. v. 66 (1997), no. 220, p. 1766–1767, v. 65 (1996), no. 215, p. 1384, v. 50 (1988), no. 182, p. 653, v. 41 (1983), no. 164, p. 778–779, v. 27 (1973), no. 122, p. 451, v. 26 (1972), no. 118, p. 599, v. 25 (1971), no. 113, p. 199, v. 24 (1970), no. 109, p. 239-240.

External Links:

MathReview (H. Kober), ZentralBlatt

Referenced by:

§1.14(viii), §10.22(vi), §10.32(iv), §10.43(vi), §10.9(iv), §11.10(x), §11.5(iii), §11.7(v), §11.9(iv), §12.12, §12.5(iv), §13.10(ii), §13.10(iii), §13.10(iv), §13.23(i), §13.23(ii), §14.17(v), §15.14, §16.20, §16.5, (18.17.21_1), (18.17.34_5), §18.17(ix), §20.10(ii), §20.10(iii), §25.5(ii), §5.13, §6.14(iii), §6.7(iv), §7.14(iii), §7.7(iii), §8.14.

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Tables of Integral Transforms. Vol. II. McGraw-Hill Book Company, Inc., New York-Toronto-London.

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Notes:

Table errata: Math. Comp. v. 65 (1996), no. 215, p. 1385, v. 41 (1983), no. 164, pp. 779–780, v. 31 (1977), no. 138, p. 614, v. 31 (1977), no. 137, pp. 328–329, v. 26 (1972), no. 118, p. 599, v. 25 (1971), no. 113, p. 199, v. 23 (1969), no. 106, p. 468.

External Links:

MathReview (H. Kober), ZentralBlatt

Referenced by:

§1.14(viii), §10.22(v), §10.22(vi), §10.43(v), §10.43(vi), §12.12, §13.10(v), §13.10(v), §13.10(vi), §13.23(iii), §13.23(v), §15.14, §15.14, §18.17(ix), §5.13, §8.14.

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The Thirteen Books of Euclid’s Elements. Cambridge University Press, Cambridge.

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Notes:

Translated from the text of Heiberg, with introduction and commentary by Thomas L. Heath. Reprint of the Cambridge Univeristy second edition by Dover Publications, Inc., New York, 1956.

External Links:

MathReview, ZentralBlatt

Referenced by:

§27.2(i).

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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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Notes:

With a loose Russian summary

External Links:

ISSN 0011-4642, MathReview (D. Hinton)

Referenced by:

§1.13(viii).

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10: 20 Theta Functions

Chapter 20 Theta Functions

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