Hill type

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1: 1.3 Determinants, Linear Operators, and Spectral Expansions

… ►Of importance for special functions are infinite determinants of Hill’s type. These have the property that the double series …Hill-type determinants always converge. …

2: Bibliography H

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Über die Integration logarithmisch-rationaler Differentiale. J. Reine Angew. Math. 3, pp. 101–159.

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ZentralBlatt

Referenced by:

§25.12(i).

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Algorithm 442: Normal deviate. Comm. ACM 16 (1), pp. 51–52.

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Notes:

Includes Algol program, minimum accuracy 24D.

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ISSN 0001-0782, Document

Referenced by:

§7.25(ii).

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Algorithm AS66: The normal integral. Appl. Statist. 22 (3), pp. 424–427.

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Notes:

Double-precision Fortran, maximum accuracy 12D.

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FullText, Code

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5th item.

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Note on some hypergeometric series of higher order. J. London Math. Soc. 4, pp. 50–54.

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Document, ZentralBlatt

Referenced by:

§16.9.

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Estimates of the stability intervals for Hill’s equation. Proc. Amer. Math. Soc. 14 (6), pp. 930–932.

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FullText, MathReview (P. Ungar), ZentralBlatt

Referenced by:

§28.29(iii).

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3: Bibliography S

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Some properties of polynomial sets of type zero. Duke Math. J. 5, pp. 590–622.

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ISSN 0012-7094, Link, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§18.2(xii).

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Introductory Complex Analysis. Prentice-Hall, Inc., Englewood Cliffs, N.J..

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Notes:

Reprinted by Dover Publications Inc. 1972

External Links:

MathReview (E. Hille), ZentralBlatt

Referenced by:

Ch.4.

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Représentation asymptotique de la solution générale de l’équation de Mathieu-Hill. Acad. Roy. Belg. Bull. Cl. Sci. (5) 51 (11), pp. 1415–1446.

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ZentralBlatt

Referenced by:

§28.8(ii).

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On inequalities of the Turán type. Math. Scand. 2, pp. 65–73.

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ISSN 0025-5521, FullText, MathReview (G. Szegő), ZentralBlatt

Referenced by:

§18.14(ii).

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Microwave Transmission. McGraw-Hill Book Co., New York.

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Notes:

Reprinted by Dover Publications Inc., New York, 1960.

External Links:

MathReview (H. Bremmer), ZentralBlatt

Referenced by:

§10.73(i).

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4: Bibliography M

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Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials. J. Comput. Appl. Math. 57 (1-2), pp. 215–237.

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ISSN 0377-0427, Document, MathReview (Leonid B. Golinskiĭ), ZentralBlatt

Referenced by:

§32.15.

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Hill’s Equation. Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons, New York-London-Sydney.

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Notes:

Reprinted by Dover Publications, Inc., New York, 1979.

External Links:

MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§1.3(iii), §28.29(i), §28.29(ii), §28.29(ii), §28.29(iii), §28.29(iii), §28.29(iii), §28.30(i), Ch.28, §29.3(i), §29.9.

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On a Kummer-type transformation for the generalized hypergeometric function ${}_2{}^{}F_2^{}$ . J. Comput. Appl. Math. 157 (2), pp. 507–509.

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ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§16.6.

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Methods of Theoretical Physics. Vol. 1, McGraw-Hill Book Co., New York.

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Notes:

Reprinted by Feshbach Publishing, http://www.feshbachpublishing.com/.

External Links:

Feshbach Publishing, MathReview (M. Pinl), ZentralBlatt

Referenced by:

§1.17(iii), §1.5(ii), §12.17, §12.17, §12.17.

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Methods of Theoretical Physics. Vol. 2, McGraw-Hill Book Co., New York.

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Notes:

Reprinted by Feshbach Publishing, http://www.feshbachpublishing.com/.

External Links:

Feshbach Publishing, MathReview (M. Pinl), ZentralBlatt

Referenced by:

§12.17, §12.17.

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5: Bibliography K

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Orthonormal polynomials with generalized Freud-type weights. J. Approx. Theory 121 (1), pp. 13–53.

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ISSN 0021-9045, Document, Link, MathReview (Walter Van Assche)

Referenced by:

§18.32.

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Algorithm 763: INTERVAL_ARITHMETIC: A Fortran 90 module for an interval data type. ACM Trans. Math. Software 22 (4), pp. 385–392.

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ISSN 0098-3500, Document, GAMS (module 763; package TOMS), ZentralBlatt

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2nd item.

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On differential equations for Sobolev-type Laguerre polynomials. Trans. Amer. Math. Soc. 350 (1), pp. 347–393.

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ISSN 0002-9947, FullText, MathReview (Hans W. Volkmer), ZentralBlatt

Referenced by:

§18.36(ii).

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Electromagnetic Fields and Relativistic Particles. International Series in Pure and Applied Physics, McGraw-Hill Book Co., New York.

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ISBN 0-07-035264-X, MathReview (George Zipfel, Jr.)

Referenced by:

§1.17(ii), §10.73(ii).

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A new proof of a Paley-Wiener type theorem for the Jacobi transform. Ark. Mat. 13, pp. 145–159.

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Document, MathReview (G. Gasper), ZentralBlatt

Referenced by:

§18.10(i).

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6: 18.18 Sums

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§18.18(vi) Bateman-Type Sums

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Jacobi

… ►Formula (18.18.27) is known as the Hille–Hardy formula. …

7: Bibliography V

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Symbolic evaluation of coefficients in Airy-type asymptotic expansions. J. Math. Anal. Appl. 269 (1), pp. 317–331.

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ISSN 0022-247X, Document, MathReview, ZentralBlatt

Referenced by:

§2.4(v).

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Integralgleichungen für periodische Lösungen Hill’scher Differentialgleichungen. Analysis 3 (1-4), pp. 189–203 (German).

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ISSN 0174-4747, MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§28.10(iii), §29.8, §29.8.

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8: Bibliography

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Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable. 2nd edition, McGraw-Hill Book Co., New York.

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Notes:

A third edition was published in 1978 by McGraw-Hill, New York.

External Links:

MathReview (P. Lelong), ZentralBlatt

Referenced by:

§1.9(iii), §23.18.

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Szegő Type Asymptotics for the Reproducing Kernel in Spaces of Full-Plane Weighted Polynomials. Comm. Math. Phys. 398 (3), pp. 1291–1348.

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External Links:

ISSN 0010-3616, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§8.11(iii), §8.11(iii), Erratum (V1.1.10) for Section 8.11(iii).

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Multiple series Rogers-Ramanujan type identities. Pacific J. Math. 114 (2), pp. 267–283.

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ISSN 0030-8730, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§17.12.

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The Whittaker-Hill equation and the wave equation in paraboloidal co-ordinates. Proc. Roy. Soc. Edinburgh Sect. A 67, pp. 265–276.

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External Links:

MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§28.31(i), §28.31(ii), §28.31(ii), §28.32(ii).

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

Referenced by:

§18.18(iv).

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9: Bibliography P

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Signal Analysis. McGraw-Hill, New York.

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External Links:

ISBN 00-704-8460-0, 00-706-6468-4, ZentralBlatt

Referenced by:

§30.15(ii), §30.15(iii), §30.15(iv), §30.15(v), §30.15(v).

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A Kummer-type transformation for a ${}_2{}^{}F_2^{}$ hypergeometric function. J. Comput. Appl. Math. 173 (2), pp. 379–382.

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

Referenced by:

§16.6.

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Voronoi type congruences for Bernoulli numbers. In Voronoi’s Impact on Modern Science. Book I, P. Engel and H. Syta (Eds.),

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ZentralBlatt

Referenced by:

§24.10(iii).

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