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11: Bibliography E

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Integral Representation and the Computation of Combinatorial Sums. Translations of Mathematical Monographs, Vol. 59, American Mathematical Society, Providence, RI.

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Notes:

Translated from the Russian by H. H. McFadden, Translation edited by Lev J. Leifman

External Links:

ISBN 0-8218-4512-8, MathReview, ZentralBlatt

Referenced by:

§15.17(iv).

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On the representations of a number as a sum of three squares. Proc. London Math. Soc. (3) 9, pp. 575–594.

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Document, MathReview (S. Chowla), ZentralBlatt

Referenced by:

§20.12(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

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ISSN 0011-4642, MathReview (D. Hinton)

Referenced by:

§1.13(viii).

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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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External Links:

Document, Link, MathReview Entry

Referenced by:

§1.18(ix), §1.18(x).

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A new series representation for $\zeta (3)$ . Amer. Math. Monthly 97 (3), pp. 219–220.

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ISSN 0002-9890, FullText, MathReview (Christian Radoux), ZentralBlatt

Referenced by:

(25.8.10).

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12: Bibliography R

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A non-negative representation of the linearization coefficients of the product of Jacobi polynomials. Canad. J. Math. 33 (4), pp. 915–928.

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ISSN 0008-414X, Document, Link, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.18(v).

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Integral representations for products of Airy functions. Z. Angew. Math. Phys. 46 (2), pp. 159–170.

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ISSN 0044-2275, Document, MathReview (P. K. Banerji), ZentralBlatt

Referenced by:

§9.11(iii), §9.11(v), §9.11(v), (9.5.6), §9.5(ii).

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Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse. Inauguraldissertation, Göttingen.

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Referenced by:

§21.7(i).

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Elementary Number Theory and its Applications. 5th edition, Addison-Wesley, Reading, MA.

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ISBN 0-201-87073-8, MathReview (Norman J. Richert)

Referenced by:

§27.17.

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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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Document, MathReview (M. A. Harrison), ZentralBlatt

Referenced by:

§27.5.

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13: 27.14 Unrestricted Partitions

… ►Euler’s pentagonal number theorem states that … ►and $s(h,k)$ is a Dedekind sum given by … ►For example, the Ramanujan identity … ►

§27.14(vi) Ramanujan’s Tau Function

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14: 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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External Links:

MathReview (J. Browkin), ZentralBlatt

Referenced by:

§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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Referenced by:

§35.7(ii).

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15: Bibliography H

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Quantum theory for mathematicians. Graduate Texts in Mathematics, Vol. 267, Springer, New York.

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ISBN 978-1-4614-7115-8; 978-1-4614-7116-5, Document, Link, MathReview Entry

Referenced by:

§1.18(x).

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Lie groups, Lie algebras, and representations. Second edition, Graduate Texts in Mathematics, Vol. 222, Springer, Cham.

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Notes:

An elementary introduction

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ISBN 978-3-319-13466-6; 978-3-319-13467-3, Document, Link, MathReview Entry

Referenced by:

§1.2(vi).

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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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External Links:

ISBN 0-19-853170-2; 0-19-853171-0, MathReview (T. M. Apostol), ZentralBlatt

Referenced by:

§20.12(i), Ch.27.

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Molecular Electronic-Structure Theory. John Wiley & Sons, New York.

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Notes:

Paperback Reprint of 2004 Edition

External Links:

ISBN 9871118531471

Referenced by:

§18.39(iii).

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The Theory of Spherical and Ellipsoidal Harmonics. Cambridge University Press, London-New York.

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Notes:

Reprinted by Chelsea Publishing Company, New York, 1955 and 1965.

External Links:

ISBN 0-8284-0104-7, MathReview, ZentralBlatt

Referenced by:

§14.1, §14.11, §14.16(ii), §14.16(iii), §14.20(x), §14.27, §14.27, §14.3(i), §14.3(i), Ch.14, §29.18(iii), Ch.29.

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16: Bibliography C

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Introduction to the Theory of Fourier’s Series and Integrals. 3rd edition, Macmillan, London.

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Notes:

Reprinted by Dover, New York, 1950.

External Links:

ZentralBlatt

Referenced by:

§6.16(i).

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The Mathematical Theory of Black Holes. In General Relativity and Gravitation (Padova, 1983), pp. 5–26.

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External Links:

MathReview Entry

Referenced by:

§31.17(ii).

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Introduction to Approximation Theory. 2nd edition, Chelsea Publishing Co., New York.

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Notes:

Reprinted by AMS Chelsea Publishing, Providence, RI, 1998

External Links:

ISBN 0-8218-1374-9, MathReview, ZentralBlatt

Referenced by:

§18.38(i).

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Theory of ordinary differential equations. McGraw-Hill Book Company, Inc., New York-Toronto-London.

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External Links:

MathReview (M. Zlámal)

Referenced by:

§1.18(ix), §1.18(x).

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A Course in Computational Algebraic Number Theory. Springer-Verlag, Berlin-New York.

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External Links:

ISBN 3-540-55640-0, 0-387-55640-0, MathReview (Joe P. Buhler), ZentralBlatt

Referenced by:

§23.17(i), §27.18, §27.18.

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17: Bibliography

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Theory of Incomplete Cylindrical Functions and Their Applications. Springer-Verlag, Berlin.

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Notes:

Translated from the Russian by H. E. Fettis, J. W. Goresh and D. A. Lee, Die Grundlehren der mathematischen Wissenschaften, Band 160

External Links:

MathReview, ZentralBlatt

Referenced by:

1st item.

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Integral representation of Kelvin functions and their derivatives with respect to the order. Z. Angew. Math. Phys. 42 (5), pp. 708–714.

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ISSN 0044-2275, Document, MathReview (A. de Castro Brzezicki), ZentralBlatt

Referenced by:

§10.61(v), §10.64.

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Number Theory. In The New Encyclopaedia Britannica, Vol. 25, pp. 14–37.

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Referenced by:

§27.13(i), §27.15, §27.16, Ch.27.

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Integral representations for Jacobi polynomials and some applications. J. Math. Anal. Appl. 26 (2), pp. 411–437.

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External Links:

Document, MathReview (D. L. Colton), ZentralBlatt

Referenced by:

§18.17(iv).

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Jacobi polynomials. I. New proofs of Koornwinder’s Laplace type integral representation and Bateman’s bilinear sum. SIAM J. Math. Anal. 5, pp. 119–124.

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External Links:

ISSN 1095-7154, Document, MathReview (R. P. Soni), ZentralBlatt

Referenced by:

§18.18(iv).

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18: Bibliography M

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The Theory of Groups. Clarendon Press, Oxford.

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Notes:

Reprinted in 1988 by Krieger Publishing Co., Malabar, FL

External Links:

ISBN 0-19-853137-0;0-89464-287-1, MathReview (A. P. Street), ZentralBlatt

Referenced by:

§23.20(ii).

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Zur Theorie des zylindrisch-parabolischen Spiegels. Z. Physik 118, pp. 343–356 (German).

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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§12.17.

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An integral representation for the Bessel form. J. Comput. Appl. Math. 57 (1-2), pp. 251–260.

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ISSN 0377-0427, Document, MathReview (Hans-Jürgen Glaeske), ZentralBlatt

Referenced by:

§18.34(ii).

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Loud Speakers: Theory, Performance, Testing and Design. Oxford University Press, New York.

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Notes:

Reprinted, with corrections, by Dover Publications Inc., 1960.

External Links:

MathReview, ZentralBlatt

Referenced by:

§11.12.

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An integral representation for the Lambert $W$ function.

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External Links:

2012.02480

Referenced by:

(4.13.16), §4.13.

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19: 13.27 Mathematical Applications

… ►Confluent hypergeometric functions are connected with representations of the group of third-order triangular matrices. …Vilenkin (1968, Chapter 8) constructs irreducible representations of this group, in which the diagonal matrices correspond to operators of multiplication by an exponential function. … ►For applications of Whittaker functions to the uniform asymptotic theory of differential equations with a coalescing turning point and simple pole see §§2.8(vi) and 18.15(i). …

20: Bibliography S

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The Laplace Transform: Theory and Applications. Undergraduate Texts in Mathematics, Springer-Verlag, New York.

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External Links:

ISBN 0-387-98698-7, MathReview (Philip Heywood), ZentralBlatt

Referenced by:

§1.14(iii), §1.14(vii).

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Quantum defect theory. Rep. Prog. Phys. 46 (2), pp. 167–257.

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External Links:

Document

Referenced by:

§33.14(i), §33.22(ii).

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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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Über die analytische Theorie der quadratischen Formen. Ann. of Math. (2) 36 (3), pp. 527–606.

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External Links:

ISSN 0003-486X, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§35.2.

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Large orders and summability of eigenvalue perturbation theory: A mathematical overview. Int. J. Quantum Chem. 21, pp. 3–25.

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External Links:

Document

Referenced by:

§22.19(ii).

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