Bibliography H

♦A♦B♦C♦D♦E♦F♦G♦H♦I♦J♦K♦L♦M♦N♦O♦P♦Q♦R♦S♦T♦U♦V♦W♦X♦Y♦Z♦

L. Habsieger (1986)
La $q$ -conjecture de Macdonald-Morris pour $G_{2}$ ,

C. R. Acad. Sci. Paris Sér. I Math. 303 (6), pp. 211–213 (French).

External Links:

ISSN 0249-6291, MathReview (David M. Bressoud), ZentralBlatt.

Referenced by:

¶ ‣ §17.14.

Encodings:

BibTeX
L. Habsieger (1988)
Une $q$ -intégrale de Selberg et Askey,

SIAM J. Math. Anal. 19 (6), pp. 1475–1489.

External Links:

ISSN 0036-1410, Document, MathReview (R. A. Askey), ZentralBlatt.

Referenced by:

¶ ‣ §17.13.

Encodings:

BibTeX
J. Hadamard (1896)
Sur la distribution des zéros de la fonction $\mathop{\zeta\/}\nolimits(s)$ et ses conséquences arithmétiques,

Bull. Soc. Math. France 24, pp. 199–220 (French).

Notes:

Reprinted in Oeuvres de Jacques Hadamard. Tomes I, pp. 189–210, Éditions du Centre National de la Recherche Scientifique, Paris, 1968.

External Links:

ISSN 0037-9484, FullText, MathReview Entry, ZentralBlatt.

Referenced by:

§25.10(i), §27.2(i).

Encodings:

BibTeX
P. I. Hadži (1968)
Computation of certain integrals that contain a probability function.,

Bul. Akad. Štiince RSS Moldoven 1968 (2), pp. 81–104. (errata insert) (Russian).

External Links:

MathReview (H. A. Lauwerier).

Referenced by:

§7.14(iii).

Encodings:

BibTeX
P. I. Hadži (1969)
Certain integrals that contain a probability function and degenerate hypergeometric functions,

Bul. Akad. S̆tiince RSS Moldoven 1969 (2), pp. 40–47 (Russian).

External Links:

MathReview (Wazir Hasan Abdi).

Referenced by:

§7.14(iii).

Encodings:

BibTeX
P. I. Hadži (1970)
Some integrals that contain a probability function and hypergeometric functions,

Bul. Akad. Štiince RSS Moldoven 1970 (1), pp. 49–62 (Russian).

External Links:

MathReview (R. G. Langebartel).

Referenced by:

§7.14(iii).

Encodings:

BibTeX
P. I. Hadži (1972)
Certain sums that contain cylindrical functions,

Bul. Akad. Štiince RSS Moldoven. 1972 (3), pp. 75–77, 94 (Russian).

External Links:

MathReview (D. P. Gupta).

Referenced by:

§7.14(iii).

Encodings:

BibTeX
P. I. Hadži (1973)
The Laplace transform for expressions that contain a probability function,

Bul. Akad. Štiince RSS Moldoven. 1973 (2), pp. 78–80, 93 (Russian).

External Links:

MathReview (L. Berg).

Referenced by:

§7.14(iii).

Encodings:

BibTeX
P. I. Hadži (1975a)
Certain integrals that contain a probability function,

Bul. Akad. Štiince RSS Moldoven. 1975 (2), pp. 86–88, 95 (Russian).

External Links:

MathReview (C. Tanaka).

Referenced by:

§7.14(iii).

Encodings:

BibTeX
P. I. Hadži (1975b)
Integrals containing the Fresnel functions $S(x)$ and $C(x)$ ,

Bul. Akad. Štiince RSS Moldoven. 1975 (3), pp. 48–60, 93 (Russian).

External Links:

MathReview (J. Kaczmarski).

Referenced by:

§7.14(iii).

Encodings:

BibTeX
P. I. Hadži (1976a)
Expansions for the probability function in series of Čebyšev polynomials and Bessel functions,

Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 77–80, 96 (Russian).

External Links:

MathReview (V. L. Makarov).

Referenced by:

§7.14(iii).

Encodings:

BibTeX
P. I. Hadži (1976b)
Integrals that contain a probability function of complicated arguments,

Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 80–84, 96 (Russian).

External Links:

MathReview (V. L. Makarov).

Referenced by:

§7.14(iii).

Encodings:

BibTeX
P. I. Hadži (1978)
Sums with cylindrical functions that reduce to the probability function and to related functions,

Bul. Akad. Shtiintse RSS Moldoven. 1978 (3), pp. 80–84, 95 (Russian).

External Links:

MathReview (M. Lawrence Glasser).

Referenced by:

§7.14(iii).

Encodings:

BibTeX
E. Hahn (1980)
Asymptotik bei Jacobi-Polynomen und Jacobi-Funktionen,

Math. Z. 171 (3), pp. 201–226 (German).

External Links:

ISSN 0025-5874, Document, MathReview (R. A. Askey), ZentralBlatt.

Referenced by:

§18.15(i).

Encodings:

BibTeX
W. Hahn (1949)
Über Orthogonalpolynome, die $q$ -Differenzengleichungen genügen,

Math. Nachr. 2, pp. 4–34 (German).

External Links:

MathReview (N. J. Fine), ZentralBlatt.

Referenced by:

§18.27(i).

Encodings:

BibTeX
E. Hairer, S. P. Nørsett and G. Wanner (1993)
Solving Ordinary Differential Equations. I. Nonstiff Problems,

2nd edition, Springer Series in Computational Mathematics, Vol. 8, Springer-Verlag, Berlin.

Notes:

A reprinting with corrections appeared in 2000.

External Links:

ISBN 3-540-56670-8, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §3.7(v), §3.7(i).

Encodings:

BibTeX
E. Hairer, S. P. Nørsett and G. Wanner (2000)
Solving Ordinary Differential Equations. I. Nonstiff Problems,

2nd edition, Springer-Verlag, Berlin.

External Links:

ISBN 3-540-56670-8, Document, MathReview.

Referenced by:

§32.17.

Encodings:

BibTeX
E. Hairer and G. Wanner (1996)
Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems,

2nd edition, Springer Series in Computational Mathematics, Vol. 14, Springer-Verlag, Berlin.

External Links:

ISBN 3-540-60452-9, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §3.7(v).

Encodings:

BibTeX
R. L. Hall, N. Saad and K. D. Sen (2010)
Soft-core Coulomb potentials and Heun’s differential equation,

J. Math. Phys. 51 (Art. ID 022107, 19 pages).

External Links:

ISSN 0022-2488, Document, FullText, MathReview Entry.

Referenced by:

§31.17(ii), §31.17(ii).

Encodings:

BibTeX
M. H. Halley, D. Delande and K. T. Taylor (1993)
The combination of $R$ -matrix and complex coordinate methods: Application to the diamagnetic Rydberg spectra of Ba and Sr,

J. Phys. B 26 (12), pp. 1775–1790.

External Links:

ISSN 0953-4075, Document, MathReview.

Referenced by:

§33.22(vii).

Encodings:

BibTeX
A. J. S. Hamilton (2001)
Formulae for growth factors in expanding universes containing matter and a cosmological constant,

Monthly Notices Roy. Astronom. Soc. 322 (2), pp. 419–425.

External Links:

Document.

Referenced by:

§8.24(ii).

Encodings:

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J. Hammack, D. McCallister, N. Scheffner and H. Segur (1995)
Two-dimensional periodic waves in shallow water. II. Asymmetric waves,

J. Fluid Mech. 285, pp. 95–122.

External Links:

ISSN 0022-1120, Document, MathReview.

Referenced by:

Figure 21.9.1, Figure 21.9.1, Figure 21.9.2, Figure 21.9.2, §21.9, Sidebar 21.SB1, Sidebar 21.SB2.

Encodings:

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J. Hammack, N. Scheffner and H. Segur (1989)
Two-dimensional periodic waves in shallow water,

J. Fluid Mech. 209, pp. 567–589.

External Links:

ISSN 0022-1120, Document, MathReview.

Referenced by:

§21.9, Sidebar 21.SB2.

Encodings:

BibTeX
H. Hancock (1958)
Elliptic Integrals,

Dover Publications Inc., New York.

Notes:

Unaltered reprint of original edition published by Wiley, New York, 1917.

External Links:

MathReview Entry, ZentralBlatt.

Referenced by:

§19.8(ii).

Encodings:

BibTeX
R. A. Handelsman and J. S. Lew (1970)
Asymptotic expansion of Laplace transforms near the origin,

SIAM J. Math. Anal. 1 (1), pp. 118–130.

External Links:

Document, MathReview (E. Riekstiņš), ZentralBlatt.

Referenced by:

¶ ‣ §2.5(iii), §2.5(ii).

Encodings:

BibTeX
R. A. Handelsman and J. S. Lew (1971)
Asymptotic expansion of a class of integral transforms with algebraically dominated kernels,

J. Math. Anal. Appl. 35 (2), pp. 405–433.

External Links:

Document, MathReview (E. L. Koh), ZentralBlatt.

Referenced by:

§2.5(ii).

Encodings:

BibTeX
S. Hanish, R. V. Baier, A. L. Van Buren and B. J. King (1970)
Tables of Radial Spheroidal Wave Functions, Vols. 1-3, Prolate, $m=0,1,2$ ; Vols. 4-6, Oblate, $m=0,1,2$ ,

Technical report

Naval Research Laboratory, Washington, D.C..

Notes:

NRL Reports 7088-7093

External Links:

ZentralBlatt.

Referenced by:

§30.17.

Encodings:

BibTeX
E. R. Hansen (1975)
A Table of Series and Products,

Prentice-Hall, Englewood Cliffs, NJ.

Notes:

Table erratum: Math. Comp. v.47 (1986), no. 176, p. 767.

External Links:

ZentralBlatt.

Referenced by:

§10.23(iv), §10.44(iv), §10.60(iv), §10.65(iv), §11.10(x), §11.7(v), §12.13(ii), §13.11, §14.18(iv), §15.15, §18.18(ix), §24.14(iii), §25.11(xi), §25.8, §4.11, §4.27, §4.41, §5.16, §6.15, §7.15, §8.17(vi).

Encodings:

BibTeX
E. W. Hansen (1985)
Fast Hankel transform algorithm,

IEEE Trans. Acoust. Speech Signal Process. 32 (3), pp. 666–671.

External Links:

ISSN 0096-3518, FullText, ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

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J. Happel and H. Brenner (1973)
Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media,

2nd edition, Noordhoff International Publishing, Leyden.

Notes:

The first edition was published in 1965 by Prentice-Hall. The 2nd edition was reissued in 1983 by Springer, and in 1986 by Martinus Nijhoff Publishers (Kluwer Academic Publishers Group).

External Links:

MathReview (Chia-Shun Yih), ZentralBlatt.

Referenced by:

§10.73(i).

Encodings:

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G. H. Hardy, J. E. Littlewood and G. Pólya (1967)
Inequalities,

2nd edition, Cambridge Mathematical Library, Cambridge University Press, Cambridge.

Notes:

Reprint of the 1952 edition and reprinted in 1988.

External Links:

ISBN 0-521-35880-9, MathReview, ZentralBlatt.

Referenced by:

§1.2(iv), §1.4(viii), §1.7(i), §1.7(ii), §1.7(iii), §1.7(iv), §4.5(i), §4.5(ii).

Encodings:

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G. H. Hardy and J. E. Littlewood (1925)
Some problems of “Partitio Numerorum” (VI): Further researches in Waring’s Problem,

Math. Z. 23, pp. 1–37.

Notes:

Reprinted in Collected Papers of G. H. Hardy (Including Joint papers with J. E. Littlewood and others), Vol. I, pp. 469–505, Clarendon Press, Oxford, 1966.

External Links:

ISSN 0025-5874, Document, MathReview Entry, ZentralBlatt.

Referenced by:

§27.13(iii).

Encodings:

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G. H. Hardy and S. Ramanujan (1918)
Asymptotic formulae in combinatory analysis,

Proc. London Math. Soc. (2) 17, pp. 75–115.

Notes:

Reprinted in Ramanujan (1962, pp. 276–309).

External Links:

Document, MathReview Entry, ZentralBlatt.

Referenced by:

§27.14(iii).

Encodings:

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G. H. Hardy and E. M. Wright (1979)
An Introduction to the Theory of Numbers,

5th edition, The Clarendon Press Oxford University Press, New York-Oxford.

External Links:

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

Referenced by:

§20.12(i), Ch.27.

Encodings:

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G. H. Hardy (1912)
Note on Dr. Vacca’s series for $\gamma$ ,

Quart. J. Math. 43, pp. 215–216.

External Links:

ZentralBlatt.

Referenced by:

§25.2(ii).

Encodings:

BibTeX
G. H. Hardy (1940)
Ramanujan. Twelve Lectures on Subjects Suggested by His Life and Work,

Cambridge University Press, Cambridge, England.

Notes:

Reprinted by Chelsea Publishing Company, New York, 1959.

External Links:

MathReview (H. Rademacher), ZentralBlatt.

Referenced by:

§27.13(iv).

Encodings:

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G. H. Hardy (1949)
Divergent Series,

Clarendon Press, Oxford.

Notes:

Reprinted by the American Mathematical Society in 2000.

External Links:

MathReview (R. P. Agnew), ZentralBlatt.

Referenced by:

§1.15(ii), §1.15(viii).

Encodings:

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G. H. Hardy (1952)
A Course of Pure Mathematics,

10th edition, Cambridge University Press.

Notes:

Numerous reprintings exist, including the Centenary Edition with Foreword by T. W. Körner (Cambridge Univerity Press, 2008).

External Links:

MathReview, ZentralBlatt.

Referenced by:

§1.4(ii), §1.4(iii), §1.4(iv), §1.4(v), §1.4(vi), §1.4(vii), §4.4(iii), §4.6(i), §4.6(ii).

Encodings:

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B. A. Hargrave and B. D. Sleeman (1977)
Lamé polynomials of large order,

SIAM J. Math. Anal. 8 (5), pp. 800–842.

External Links:

Document, MathReview (F. M. Arscott), ZentralBlatt.

Referenced by:

§29.16.

Encodings:

BibTeX
B. A. Hargrave (1978)
High frequency solutions of the delta wing equations,

Proc. Roy. Soc. Edinburgh Sect. A 81 (3-4), pp. 299–316.

External Links:

ISSN 0308-2105, MathReview (V. M. Babich), ZentralBlatt.

Referenced by:

§29.19(ii).

Encodings:

BibTeX
F. E. Harris (2000)
Spherical Bessel expansions of sine, cosine, and exponential integrals,

Appl. Numer. Math. 34 (1), pp. 95–98.

External Links:

ISSN 0168-9274, Document, MathReview, ZentralBlatt.

Referenced by:

§10.60(iii), §6.10(ii), §6.15.

Encodings:

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F. E. Harris (2002)
Analytic evaluation of two-center STO electron repulsion integrals via ellipsoidal expansion,

Internat. J. Quantum Chem. 88 (6), pp. 701–734.

External Links:

Document.

Referenced by:

§8.24(iii).

Encodings:

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J. F. Hart, E. W. Cheney, C. L. Lawson, H. J. Maehly, C. K. Mesztenyi, J. R. Rice, H. G. Thacher, Jr. and C. Witzgall (1968)
Computer Approximations,

SIAM Ser. in Appl. Math., John Wiley & Sons Inc., New York.

Notes:

Reprinted by Krieger Publishing Company, 1978.

External Links:

ZentralBlatt.

Referenced by:

§3.11(i), §3.11(iii), §4.47(ii), §5.23(i), §5.23(i).

Encodings:

BibTeX
D. R. Hartree (1936)
Some properties and applications of the repeated integrals of the error function,

Proc. Manchester Lit. Philos. Soc. 80, pp. 85–102.

External Links:

ZentralBlatt.

Referenced by:

§7.18(iii), §7.18(iv), §7.18(v), §7.18(vi).

Encodings:

BibTeX
Harvard University (1945)
Tables of the Modified Hankel Functions of Order One-Third and of their Derivatives,

Harvard University Press, Cambridge, MA.

External Links:

MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§9.18(iii).

Encodings:

BibTeX
A. Hasegawa (1989)
Optical Solitons in Fibers,

Springer-Verlag, Berlin, Germany.

External Links:

ISBN 0387506683.

Referenced by:

§22.19(iii).

Encodings:

BibTeX
C. B. Haselgrove and J. C. P. Miller (1960)
Tables of the Riemann Zeta Function,

Royal Society Mathematical Tables, Vol. 6, Cambridge University Press, New York.

External Links:

MathReview (D. H. Lehmer), ZentralBlatt.

Referenced by:

§25.18(i), §25.18(ii).

Encodings:

BibTeX
C. Hastings (1955)
Approximations for Digital Computers,

Princeton University Press, Princeton, N. J..

Notes:

Assisted by Jeanne T. Hayward and James P. Wong, Jr.

External Links:

MathReview (P. W. Ketchum), ZentralBlatt.

Referenced by:

§6.20(i), §7.24(i).

Encodings:

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S. P. Hastings and J. B. McLeod (1980)
A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation,

Arch. Rational Mech. Anal. 73 (1), pp. 31–51.

External Links:

ISSN 0003-9527, Document, MathReview (Richard Brown), ZentralBlatt.

Referenced by:

§32.11(ii).

Encodings:

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H. J. Haubold, A. M. Mathai and R. K. Saxena (2011)
Mittag-Leffler functions and their applications,

J. Appl. Math. (Art. ID 298628, 51 pages).

External Links:

ISSN 1110-757X, Document, FullText, MathReview (Rudolf Gorenflo), ZentralBlatt.

Referenced by:

§10.46, §10.46.

Encodings:

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M. Hauss (1997)
An Euler-Maclaurin-type formula involving conjugate Bernoulli polynomials and an application to $\zeta(2m+1)$ ,

Commun. Appl. Anal. 1 (1), pp. 15–32.

External Links:

ISSN 1083-2564, MathReview (Pavel Guerzhoy), ZentralBlatt.

Referenced by:

§24.16(iii).

Encodings:

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M. Hauss (1998)
A Boole-type Formula involving Conjugate Euler Polynomials,

in Charlemagne and his Heritage. 1200 Years of Civilization and Science in Europe, Vol. 2 (Aachen, 1995),

(H. Th. Jongen and W. Oberschelp Eds.), pp. 361–375.

External Links:

ISBN 2-503-50674-7, MathReview (Bruce C. Berndt), ZentralBlatt.

Referenced by:

§24.16(iii).

Encodings:

BibTeX
B. Hayes (2009)
The higher arithmetic,

American Scientist 97, pp. 364–368.

External Links:

FulText.

Referenced by:

§3.1(iv).

Encodings:

BibTeX
V. B. Headley and V. K. Barwell (1975)
On the distribution of the zeros of generalized Airy functions,

Math. Comp. 29 (131), pp. 863–877.

External Links:

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

Referenced by:

§9.13(i).

Encodings:

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G. J. Heckman (1991)
An elementary approach to the hypergeometric shift operators of Opdam,

Invent. Math. 103 (2), pp. 341–350.

External Links:

ISSN 0020-9910, Document, MathReview (Eric M. Opdam), ZentralBlatt.

Referenced by:

§18.37(iii).

Encodings:

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M. Heil (1995)
Numerical Tools for the Study of Finite Gap Solutions of Integrable Systems,

Ph.D. Thesis, Technischen Universität Berlin.

Notes:

(All relevant material, plus corrections, are included in Deconinck et al. (2004).)

Referenced by:

§21.5(i).

Encodings:

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R. S. Heller (1976)
25D Table of the First One Hundred Values of $j_{{0,s}}$ , $J_{1}(j_{{0,s}})$ , $j_{{1,s}}$ , $J_{0}(j_{{1,s}})=J_{0}(j^{{\prime}}_{{0,s+1}})$ , $j^{{\prime}}_{{1,s}}$ , $J_{1}(j^{{\prime}}_{{1,s}})$ ,

Technical report

Department of Physics, Worcester Polytechnic Institute, Worcester, MA.

Notes:

Ms. of six pages deposited in the UMT file

Referenced by:

¶ ‣ §10.75(iii).

Encodings:

BibTeX

E. Hendriksen and H. van Rossum (1986)
Orthogonal Laurent polynomials,

Nederl. Akad. Wetensch. Indag. Math. 48 (1), pp. 17–36.

External Links:

ISSN 0019-3577, Document, MathReview (W. J. Thron), ZentralBlatt.

Referenced by:

§18.33(v).

Encodings:

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P. Henrici (1974)
Applied and Computational Complex Analysis. Vol. 1: Power Series—Integration—Conformal Mapping—Location of Zeros,

Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York.

Notes:

Reprinted in 1988.

External Links:

ISBN 0-471-37244-7, MathReview (M. Marden), ZentralBlatt.

Referenced by:

§1.10(vii), §1.9(vi), Ch.3.

Encodings:

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P. Henrici (1977)
Applied and Computational Complex Analysis. Vol. 2: Special Functions—Integral Transforms—Asymptotics—Continued Fractions,

Wiley-Interscience [John Wiley & Sons], New York.

Notes:

Reprinted in 1991.

External Links:

ISBN 0-471-01525-3, MathReview (A. E. Heins), ZentralBlatt.

Referenced by:

§1.11(v), Ch.3.

Encodings:

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P. Henrici (1986)
Applied and Computational Complex Analysis. Vol. 3: Discrete Fourier Analysis—Cauchy Integrals—Construction of Conformal Maps—Univalent Functions,

Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons Inc.], New York.

Notes:

Reprinted in 1993.

External Links:

ISBN 0-471-08703-3; 0-471-58986-1, MathReview (A. E. Heins), ZentralBlatt.

Referenced by:

§1.14(v), Ch.3.

Encodings:

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J. R. Herndon (1961a)
Algorithm 55: Complete elliptic integral of the first kind,

Comm. ACM 4 (4), pp. 180.

Notes:

Includes Algol program, maximum accuracy 8D. For certification see same journal 6 (1966), pp. 166–167

External Links:

ISSN 0001-0782, Document.

Referenced by:

§19.39(ii).

Encodings:

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J. R. Herndon (1961b)
Algorithm 56: Complete elliptic integral of the second kind,

Comm. ACM 4 (4), pp. 180–181.

Notes:

Includes Algol program, maximum accuracy 8D. For certification see same journal 9 (1966), p. 12

External Links:

ISSN 0001-0782, Document.

Referenced by:

§19.39(ii).

Encodings:

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D. R. Herrick and S. O’Connor (1998)
Inverse virial symmetry of diatomic potential curves,

J. Chem. Phys. 109 (1), pp. 11–19.

External Links:

Document.

Referenced by:

§15.18.

Encodings:

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C. S. Herz (1955)
Bessel functions of matrix argument,

Ann. of Math. (2) 61 (3), pp. 474–523.

External Links:

FullText, MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§35.1, §35.2, §35.3(ii), §35.5(i), §35.5(ii), §35.5(iii), §35.6(i), §35.6(ii), §35.6(iii), §35.6(iv), §35.7(i), §35.7(ii), §35.7(iv), ¶ ‣ §35.8(i), §35.8(ii), §35.8(iv), Ch.35.

Encodings:

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H. W. Hethcote (1970)
Error bounds for asymptotic approximations of zeros of Hankel functions occurring in diffraction problems,

J. Mathematical Phys. 11 (8), pp. 2501–2504.

External Links:

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

Referenced by:

§10.21(xiv).

Encodings:

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D. Hilbert (1909)
Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl $n^{\mathrm{ter}}$ Potenzen (Waringsches Problem),

Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, pp. 17–36 (German).

Notes:

Also in Math. Annalen (1909), v. 67, pp. 281–300.

External Links:

Document, MathReview Entry, ZentralBlatt.

Referenced by:

§27.13(iii).

Encodings:

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F. B. Hildebrand (1974)
Introduction to Numerical Analysis,

2nd edition, McGraw-Hill Book Co., New York.

Notes:

Reprinted by Dover Publications Inc., New York, 1987.

External Links:

ISBN 0-486-65363-3, MathReview, ZentralBlatt.

Referenced by:

§3.3(iii), §3.3(iv), §3.3(v), §3.4(i), §3.8(v), Ch.3.

Encodings:

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C. J. Hill (1828)
Über die Integration logarithmisch-rationaler Differentiale,

J. Reine Angew. Math. 3, pp. 101–159.

External Links:

ZentralBlatt.

Referenced by:

§25.12(i).

Encodings:

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G. W. Hill and A. W. Davis (1973)
Algorithm 442: Normal deviate,

Comm. ACM 16 (1), pp. 51–52.

Notes:

Includes Algol program, minimum accuracy 24D.

External Links:

ISSN 0001-0782, Document.

Referenced by:

§7.25(ii).

Encodings:

BibTeX
G. W. Hill (1970)
Algorithm 395: Student’s t-distribution,

Comm. ACM 13 (10), pp. 617–619.

Notes:

Includes Algol program, maximum accuracy 11S. For Remarks see ACM Trans. Math. Software 5(1979) and 7(1981)

External Links:

ISSN 0001-0782, Document, Remark 1, Remark 2.

Referenced by:

§8.28(iv).

Encodings:

BibTeX
G. W. Hill (1981)
Algorithm 571: Statistics for von Mises’ and Fisher’s distributions of directions: $I_{1}(x)/I_{0}(x)$ , $I_{{1.5}}(x)/I_{{0.5}}(x)$ and their inverses [S14],

ACM Trans. Math. Software 7 (2), pp. 233–238.

Notes:

Single-precision Fortran, minimum accuracy 8S.

External Links:

ISSN 0098-3500, Document, TOMS module 571 (in GAMS).

Referenced by:

§10.77(ii).

Encodings:

BibTeX
I. D. Hill (1973)
Algorithm AS66: The normal integral,

Appl. Statist. 22 (3), pp. 424–427.

Notes:

Double-precision Fortran, maximum accuracy 12D.

External Links:

FullText, Code.

Referenced by:

§7.25(ii).

Encodings:

BibTeX
E. Hille (1929)
Note on some hypergeometric series of higher order,

J. London Math. Soc. 4, pp. 50–54.

External Links:

Document, ZentralBlatt.

Referenced by:

§16.9.

Encodings:

BibTeX
E. Hille (1976)
Ordinary Differential Equations in the Complex Domain,

Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York.

Notes:

Reprinted by Dover Publications Inc., New York, 1997

External Links:

ISBN 0-471-39964-7, MathReview (S. Strelitz), ZentralBlatt.

Referenced by:

§16.8(i), §32.2(i).

Encodings:

BibTeX
P. Hillion (1997)
Diffraction and Weber functions,

SIAM J. Appl. Math. 57 (6), pp. 1702–1715.

External Links:

ISSN 0036-1399, Document, MathReview, ZentralBlatt.

Referenced by:

§12.13(ii), §12.17.

Encodings:

BibTeX
M. H. Hirata (1975)
Flow near the bow of a steadily turning ship,

J. Fluid Mech. 71 (2), pp. 283–291.

External Links:

Document, ZentralBlatt.

Referenced by:

§11.12.

Encodings:

BibTeX
N. J. Hitchin (1995)
Poncelet Polygons and the Painlevé Equations,

in Geometry and Analysis (Bombay, 1992),

pp. 151–185.

External Links:

MathReview (Henrik Pedersen), ZentralBlatt.

Referenced by:

§32.9(iii).

Encodings:

BibTeX
N. J. Hitchin (2003)
A lecture on the octahedron,

Bull. London Math. Soc. 35 (5), pp. 577–600.

External Links:

ISSN 0024-6093, Document, MathReview (I. Dolgachev), ZentralBlatt.

Referenced by:

§32.9(iii).

Encodings:

BibTeX
M. Hiyama and H. Nakamura (1997)
Two-center Coulomb functions,

Comput. Phys. Comm. 103 (2-3), pp. 209–216.

Notes:

Double-precision Fortran code.

External Links:

ISSN 0010-4655, Document, Code.

Referenced by:

§33.26(ii).

Encodings:

BibTeX
E. W. Hobson (1928)
A Treatise on Plane and Advanced Trigonometry,

7th edition, Cambridge University Press.

Notes:

Reprinted by Dover Publications Inc., New York, 2004.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§4.16, §4.17, §4.19, §4.2(ii), §4.2(iii), §4.21(i), §4.21(ii), §4.21(iii), §4.21(iv), §4.22, §4.23(v), §4.23(vi), §4.24(i), §4.24(iii), §4.28, §4.30, §4.31, §4.35(i), §4.35(ii), §4.35(iii), §4.35(iv), §4.42(i), §4.42(ii), §4.43, §4.8(ii), Ch.4.

Encodings:

BibTeX
E. W. Hobson (1931)
The Theory of Spherical and Ellipsoidal Harmonics,

Cambridge University Press, London-New York.

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.

Encodings:

BibTeX
H. Hochstadt (1963)
Estimates of the stability intervals for Hill’s equation,

Proc. Amer. Math. Soc. 14 (6), pp. 930–932.

External Links:

FullText, MathReview (P. Ungar), ZentralBlatt.

Referenced by:

§28.29(iii).

Encodings:

BibTeX
H. Hochstadt (1964)
Differential Equations: A Modern Approach,

Holt, Rinehart and Winston, New York.

Notes:

Reprinted by Dover in 1975.

External Links:

MathReview (Z. Opial), ZentralBlatt.

Referenced by:

§29.3(vi).

Encodings:

BibTeX
H. Hochstadt (1971)
The Functions of Mathematical Physics,

Wiley-Interscience [John Wiley & Sons, Inc.], New York-London-Sydney.

Notes:

Pure and Applied Mathematics, Vol. XXIII. Reprinted with corrections by Dover Publications Inc., New York, 1986.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§13.28(i), Ch.13, §15.17(ii), Ch.15.

Encodings:

BibTeX
L. E. Hoisington and G. Breit (1938)
Calculation of Coulomb wave functions for high energies,

Phys. Rev. 54 (8), pp. 627–628.

External Links:

Document.

Referenced by:

§33.7.

Encodings:

BibTeX
P. Holmes and D. Spence (1984)
On a Painlevé-type boundary-value problem,

Quart. J. Mech. Appl. Math. 37 (4), pp. 525–538.

External Links:

ISSN 0033-5614, Document, MathReview, ZentralBlatt.

Referenced by:

§32.11(i), §32.17.

Encodings:

BibTeX
E. Hopf (1934)
Mathematical Problems of Radiative Equilibrium,

Cambridge Tracts in Mathematics and Mathematical Physics No. 31, Cambridge University Press, Cambridge.

Notes:

Reprinted by Stechert-Hafner, Inc., New York, 1964

External Links:

MathReview, ZentralBlatt.

Referenced by:

§8.19(ix), §8.24(iii).

Encodings:

BibTeX
K. Horata (1989)
An explicit formula for Bernoulli numbers,

Rep. Fac. Sci. Technol. Meijo Univ. 29, pp. 1–6.

External Links:

ZentralBlatt.

Referenced by:

§24.6.

Encodings:

BibTeX
K. Horata (1991)
On congruences involving Bernoulli numbers and irregular primes. II,

Rep. Fac. Sci. Technol. Meijo Univ. 31, pp. 1–8.

External Links:

ZentralBlatt.

Referenced by:

§24.15(iii).

Encodings:

BibTeX
F. T. Howard (1976)
Roots of the Euler polynomials,

Pacific J. Math. 64 (1), pp. 181–191.

External Links:

MathReview (M. Marden), ZentralBlatt.

Referenced by:

§24.12(ii).

Encodings:

BibTeX
F. T. Howard (1996a)
Explicit formulas for degenerate Bernoulli numbers,

Discrete Math. 162 (1-3), pp. 175–185.

External Links:

ISSN 0012-365X, Document, MathReview (L. Skula), ZentralBlatt.

Referenced by:

§24.16(i).

Encodings:

BibTeX
F. T. Howard (1996b)
Sums of powers of integers via generating functions,

Fibonacci Quart. 34 (3), pp. 244–256.

External Links:

ISSN 0015-0517, MathReview (Noriaki Kimura), ZentralBlatt.

Referenced by:

§24.4(iii).

Encodings:

BibTeX
C. J. Howls, P. J. Langman and A. B. Olde Daalhuis (2004)
On the higher-order Stokes phenomenon,

Proc. Roy. Soc. London Ser. A 460, pp. 2285–2303.

External Links:

ISSN 1364-5021, Document, MathReview (W. Balser), ZentralBlatt.

Referenced by:

§2.11(iv).

Encodings:

BibTeX
C. J. Howls and A. B. Olde Daalhuis (1999)
On the resurgence properties of the uniform asymptotic expansion of Bessel functions of large order,

Proc. Roy. Soc. London Ser. A 455, pp. 3917–3930.

External Links:

ISSN 1364-5021, Document, MathReview (A. D. Wood), ZentralBlatt.

Referenced by:

§10.20(ii).

Encodings:

BibTeX
C. J. Howls (1992)
Hyperasymptotics for integrals with finite endpoints,

Proc. Roy. Soc. London Ser. A 439, pp. 373–396.

External Links:

ISSN 0962-8444, FullText, MathReview, ZentralBlatt.

Referenced by:

§2.11(v).

Encodings:

BibTeX
M. Hoyles, S. Kuyucak and S. Chung (1998)
Solutions of Poisson’s equation in channel-like geometries,

Comput. Phys. Comm. 115 (1), pp. 45–68.

External Links:

ISSN 0010-4655, Document, Code, MathReview Entry, ZentralBlatt.

Referenced by:

§14.31(i).

Encodings:

BibTeX
Y. P. Hsu (1993)
Development of a Gaussian hypergeometric function code in complex domains,

Internat. J. Modern Phys. C 4 (4), pp. 805–840.

External Links:

ISSN 0129-1831, Document, MathReview (Walter Gautschi), ZentralBlatt.

Referenced by:

§15.20(iii).

Encodings:

BibTeX
L. K. Hua (1963)
Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains,

Translations of Mathematical Monographs, Vol. 6, American Mathematical Society, Providence, RI.

Notes:

Reprinted in 1979.

External Links:

ISBN 0-8218-1556-3, MathReview, ZentralBlatt.

Referenced by:

§35.4(i).

Encodings:

BibTeX
I. Huang and S. Huang (1999)
Bernoulli numbers and polynomials via residues,

J. Number Theory 76 (2), pp. 178–193.

External Links:

ISSN 0022-314X, Document, MathReview (L. Skula), ZentralBlatt.

Referenced by:

§24.14(ii).

Encodings:

BibTeX
J. H. Hubbard and B. B. Hubbard (2002)
Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach,

2nd edition, Prentice Hall Inc., Upper Saddle River, NJ.

External Links:

ISBN 0-13-041408-5; 978-0-13-041408-3, MathReview (W. P. Ziemer), ZentralBlatt.

Referenced by:

§1.6(i).

Encodings:

BibTeX
M. H. Hull and G. Breit (1959)
Coulomb Wave Functions,

in Handbuch der Physik, Bd. 41/1,

pp. 408–465.

External Links:

MathReview (G. Källén).

Referenced by:

§33.2(iii), §33.23(vii), §33.23(vii), §33.24, §33.5(ii), §33.7, Ch.33.

Encodings:

BibTeX
T. E. Hull and A. Abrham (1986)
Variable precision exponential function,

ACM Trans. Math. Software 12 (2), pp. 79–91.

External Links:

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

Referenced by:

§4.48(iii).

Encodings:

BibTeX
P. Humbert (1920)
Sur les fonctions hypercylindriques,

C. R. Acad. Sci. Paris Sér. I Math. 171, pp. 490–492 (French).

External Links:

ZentralBlatt.

Referenced by:

§13.1.

Encodings:

BibTeX
J. Humblet (1984)
Analytical structure and properties of Coulomb wave functions for real and complex energies,

Ann. Physics 155 (2), pp. 461–493.

External Links:

ISSN 0003-4916, Document, MathReview.

Referenced by:

§33.10(ii), §33.13, §33.22(vii).

Encodings:

BibTeX
J. Humblet (1985)
Bessel function expansions of Coulomb wave functions,

J. Math. Phys. 26 (4), pp. 656–659.

External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt.

Referenced by:

§33.10(ii), §33.10(iii), §33.14(iv), §33.9(ii), §33.9(ii).

Encodings:

BibTeX
C. Hunter and B. Guerrieri (1981)
The eigenvalues of Mathieu’s equation and their branch points,

Stud. Appl. Math. 64 (2), pp. 113–141.

External Links:

ISSN 0022-2526, MathReview (R. C. Varma), ZentralBlatt.

Referenced by:

§28.7.

Encodings:

BibTeX
C. Hunter and B. Guerrieri (1982)
The eigenvalues of the angular spheroidal wave equation,

Stud. Appl. Math. 66 (3), pp. 217–240.

External Links:

ISSN 0022-2526, MathReview, ZentralBlatt.

Referenced by:

§30.9(iii).

Encodings:

BibTeX
C. Hunter (1981)
Two Parametric Eigenvalue Problems of Differential Equations,

in Spectral Theory of Differential Operators (Birmingham, AL, 1981),

North-Holland Math. Stud., Vol. 55, pp. 233–241.

External Links:

MathReview (H. Hochstadt), ZentralBlatt.

Referenced by:

§28.7.

Encodings:

BibTeX
G. Hunter and M. Kuriyan (1976)
Asymptotic expansions of Mathieu functions in wave mechanics,

J. Comput. Phys. 21 (3), pp. 319–325.

External Links:

Document, MathReview (John P. Coleman).

Referenced by:

§28.33(iii).

Encodings:

BibTeX
A. Hurwitz (1882)
Einige Eigenschaften der Dirichletschen Functionen $F(s)=\sum(\frac{D}{n})\cdot\frac{1}{n}$ , die bei der Bestimmung der Klassenanzahlen binärer quadratischer Formen auftreten,

Zeitschrift für Math. u. Physik 27, pp. 86–101 (German).

External Links:

ZentralBlatt.

Referenced by:

§25.11(i).

Encodings:

BibTeX