Bibliography I

♦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♦

IEEE (1985)
IEEE Standard for Binary Floating-Point Arithmetic,

The Institute of Electrical and Electronics Engineers.

Notes:

ANSI/IEEE Std 754-1985. Reprinted in ACM SIGPLAN Notices v. 22, no. 2 (1987), pp. 9–25

External Links:

FullText, ISBN 1-5593-7653-8;0-7381-1165-1.

Referenced by:

¶ ‣ §3.1(i).

Encodings:

BibTeX
J. Igusa (1972)
Theta Functions,

Springer-Verlag, New York.

Notes:

Die Grundlehren der mathematischen Wissenschaften, Band 194

External Links:

ISBN 3540056998, MathReview (H. Klingen), ZentralBlatt.

Referenced by:

§21.5(ii), §21.8, Ch.21.

Encodings:

BibTeX
Y. Ikebe, Y. Kikuchi, I. Fujishiro, N. Asai, K. Takanashi and M. Harada (1993)
The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of $J_{0}(z)-iJ_{1}(z)$ and of Bessel functions $J_{m}(z)$ of any real order $m$ ,

Linear Algebra Appl. 194, pp. 35–70.

External Links:

ISSN 0024-3795, Document, MathReview (Alan L. Andrew), ZentralBlatt.

Referenced by:

¶ ‣ §10.21(ix).

Encodings:

BibTeX
Y. Ikebe, Y. Kikuchi and I. Fujishiro (1991)
Computing zeros and orders of Bessel functions,

J. Comput. Appl. Math. 38 (1-3), pp. 169–184.

External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vi), ¶ ‣ §3.8(iii).

Encodings:

BibTeX
Y. Ikebe (1975)
The zeros of regular Coulomb wave functions and of their derivatives,

Math. Comp. 29, pp. 878–887.

External Links:

ISSN 0025-5718, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §3.8(iii).

Encodings:

BibTeX
M. Ikonomou, P. Köhler and A. F. Jacob (1995)
Computation of integrals over the half-line involving products of Bessel functions, with application to microwave transmission lines,

Z. Angew. Math. Mech. 75 (12), pp. 917–926.

External Links:

ISSN 0044-2267, MathReview (John P. Coleman), ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

BibTeX
IMSL (commercial C, Fortran, and Java libraries)
Visual Numerics, Inc..

Notes:

The IMSL Libraries are large general purpose numerical software libraries with broad coverage of elementary and special functions. Implementations are in single and double precision.

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

BibTeX
E. L. Ince (1926)
Ordinary Differential Equations,

Longmans, Green and Co., London.

Notes:

Reprinted by Dover Publications, New York, 1944, 1956.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§31.12, §31.14(i), §32.2(i), §32.2(vi).

Encodings:

BibTeX
E. L. Ince (1932)
Tables of the elliptic cylinder functions,

Proc. Roy. Soc. Edinburgh Sect. A 52, pp. 355–433.

External Links:

ZentralBlatt.

Referenced by:

§28.35(i), §28.35(iii).

Encodings:

BibTeX
E. L. Ince (1940a)
The periodic Lamé functions,

Proc. Roy. Soc. Edinburgh 60, pp. 47–63.

External Links:

MathReview (H. Bateman), ZentralBlatt.

Referenced by:

§29.1, §29.15(ii), §29.21, §29.7(i).

Encodings:

BibTeX
E. L. Ince (1940b)
Further investigations into the periodic Lamé functions,

Proc. Roy. Soc. Edinburgh 60, pp. 83–99.

External Links:

MathReview (H. Bateman), ZentralBlatt.

Referenced by:

§29.1, §29.17(ii), §29.3(iii), §29.6(i), §29.6(ii), §29.6(iii), §29.6(iv), Ch.29.

Encodings:

BibTeX
A. E. Ingham (1932)
The Distribution of Prime Numbers,

Cambridge Tracts in Mathematics and Mathematical Physics, No. 30, Cambridge University Press, Cambridge.

Notes:

Reissued with a foreword by R. C. Vaughan in the Cambridge Mathematical Library series, 1990.

External Links:

ISBN 0-521-39789-8, MathReview, ZentralBlatt.

Referenced by:

§25.16(i).

Encodings:

BibTeX
A. E. Ingham (1933)
An integral which occurs in statistics,

Proceedings of the Cambridge Philosophical Society 29, pp. 271–276.

External Links:

Document, ZentralBlatt.

Referenced by:

§35.3(i), §35.3(ii).

Encodings:

BibTeX
K. Inkeri (1959)
The real roots of Bernoulli polynomials,

Ann. Univ. Turku. Ser. A I 37, pp. 1–20.

External Links:

MathReview (D. H. Lehmer), ZentralBlatt.

Referenced by:

§24.12(i).

Encodings:

BibTeX
Inverse Symbolic Calculator (Web Site)
Centre for Experimental and Constructive Mathematics, Simon Fraser University, Canada..

Notes:

From a decimal approximation, find the most likely exact value.

External Links:

Inverse Symbolic Calculator.

Referenced by:

§26.22.

Encodings:

BibTeX
K. Ireland and M. Rosen (1990)
A Classical Introduction to Modern Number Theory,

2nd edition, Springer-Verlag, New York.

External Links:

ISBN 0-387-97329-X, MathReview (Glenn Stevens), ZentralBlatt.

Referenced by:

§24.10(i), §24.10(ii), §24.10(iii), §24.17(iii).

Encodings:

BibTeX
A. Iserles, P. E. Koch, S. P. Nørsett and J. M. Sanz-Serna (1991)
On polynomials orthogonal with respect to certain Sobolev inner products,

J. Approx. Theory 65 (2), pp. 151–175.

External Links:

ISSN 0021-9045, Document, MathReview (R. A. Askey).

Referenced by:

§18.36(ii).

Encodings:

BibTeX
A. Iserles, S. P. Nørsett and S. Olver (2006)
Highly Oscillatory Quadrature: The Story So Far,

in Numerical Mathematics and Advanced Applications,

pp. 97–118.

Notes:

Proceedings of ENuMath, Santiago de Compostela (2005)

External Links:

ISBN 3-540-34287-7, MathReview, ZentralBlatt.

Referenced by:

§3.5(vii).

Encodings:

BibTeX
A. Iserles (1996)
A First Course in the Numerical Analysis of Differential Equations,

Cambridge Texts in Applied Mathematics, No. 15, Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-55376-8; 0-521-55655-4, MathReview (Luis Verde-Star), ZentralBlatt.

Referenced by:

§3.7(i).

Encodings:

BibTeX

M. E. H. Ismail, J. Letessier, G. Valent and J. Wimp (1990)
Two families of associated Wilson polynomials,

Canad. J. Math. 42 (4), pp. 659–695.

External Links:

ISSN 0008-414X, MathReview (Mizan Rahman), ZentralBlatt.

Referenced by:

§18.26(iv).

Encodings:

BibTeX
M. E. H. Ismail and D. R. Masson (1994)
$q$ -Hermite polynomials, biorthogonal rational functions, and $q$ -beta integrals,

Trans. Amer. Math. Soc. 346 (1), pp. 63–116.

External Links:

ISSN 0002-9947, FullText, MathReview (R. A. Askey), ZentralBlatt.

Referenced by:

§18.28(vii).

Encodings:

BibTeX
M. E. H. Ismail and D. R. Masson (1991)
Two families of orthogonal polynomials related to Jacobi polynomials,

Rocky Mountain J. Math. 21 (1), pp. 359–375.

External Links:

ISSN 0035-7596, MathReview (Joaquin Bustoz), ZentralBlatt.

Referenced by:

¶ ‣ §18.30.

Encodings:

BibTeX
M. E. H. Ismail and M. E. Muldoon (1995)
Bounds for the small real and purely imaginary zeros of Bessel and related functions,

Methods Appl. Anal. 2 (1), pp. 1–21.

External Links:

ISSN 1073-2772, FullText, MathReview (Andrea Laforgia).

Referenced by:

§10.21(v).

Encodings:

BibTeX
M. E. H. Ismail (1986)
Asymptotics of the Askey-Wilson and $q$ -Jacobi polynomials,

SIAM J. Math. Anal. 17 (6), pp. 1475–1482.

External Links:

ISSN 0036-1410, Document, MathReview (David M. Bressoud), ZentralBlatt.

Referenced by:

§18.29.

Encodings:

BibTeX
M. E. H. Ismail (2000a)
An electrostatics model for zeros of general orthogonal polynomials,

Pacific J. Math. 193 (2), pp. 355–369.

External Links:

ISSN 0030-8730, FullText, MathReview (T. Erber), ZentralBlatt.

Referenced by:

§18.39(ii).

Encodings:

BibTeX
M. E. H. Ismail (2000b)
More on electrostatic models for zeros of orthogonal polynomials,

Numer. Funct. Anal. Optim. 21 (1-2), pp. 191–204.

External Links:

ISSN 0163-0563, FullText, MathReview (M. E. Muldoon), ZentralBlatt.

Referenced by:

§18.39(ii).

Encodings:

BibTeX
M. E. H. Ismail (2005)
Classical and Quantum Orthogonal Polynomials in One Variable,

Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.

External Links:

ISBN 978-0-521-78201-2; 0-521-78201-5, MathReview Entry, ZentralBlatt.

Referenced by:

§18.17(ii), §18.19, §18.20(i), §18.20(ii), §18.21(ii), §18.22(i), §18.22(ii), §18.22(iii), §18.23, §18.25(i), §18.25(iii), §18.26(i), §18.26(iv), §18.27(i), §18.27(ii), §18.27(iii), §18.27(v), §18.27(vi), §18.28(i), §18.28(ii), §18.28(iii), §18.28(v), §18.28(vi), §18.28(vii), §18.28(viii), §18.34(i), §18.34(ii), §18.34(iii), §18.35(i), §18.35(ii), §18.35(iii), §18.36(iii), ¶ ‣ §18.38(ii).

Encodings:

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M. E. H. Ismail and X. Li (1992)
Bound on the extreme zeros of orthogonal polynomials,

Proc. Amer. Math. Soc. 115 (1), pp. 131–140.

External Links:

ISSN 0002-9939, Document, MathReview (E. R. Love), ZentralBlatt.

Referenced by:

(18.16.12), (18.16.13).

Encodings:

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A. R. Its, A. S. Fokas and A. A. Kapaev (1994)
On the asymptotic analysis of the Painlevé equations via the isomonodromy method,

Nonlinearity 7 (5), pp. 1291–1325.

External Links:

ISSN 0951-7715, Document, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt.

Referenced by:

§32.11(iii).

Encodings:

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A. R. Its and A. A. Kapaev (1987)
The method of isomonodromic deformations and relation formulas for the second Painlevé transcendent,

Izv. Akad. Nauk SSSR Ser. Mat. 51 (4), pp. 878–892, 912 (Russian).

Notes:

In Russian. English translation: Math. USSR-Izv. 31(1988), no. 1, pp. 193–207

External Links:

ISSN 0373-2436, Document, MathReview (Alexander A. Pankov), ZentralBlatt.

Referenced by:

§32.11(iii).

Encodings:

BibTeX
A. R. Its and A. A. Kapaev (2003)
Quasi-linear Stokes phenomenon for the second Painlevé transcendent,

Nonlinearity 16 (1), pp. 363–386.

External Links:

ISSN 0951-7715, Document, MathReview (Youmin Lu), ZentralBlatt.

Referenced by:

§32.12(ii).

Encodings:

BibTeX
A. R. Its and A. A. Kapaev (1998)
Connection formulae for the fourth Painlevé transcendent; Clarkson-McLeod solution,

J. Phys. A 31 (17), pp. 4073–4113.

External Links:

ISSN 0305-4470, Document, MathReview (Yoshitsugu Takei), ZentralBlatt.

Referenced by:

§32.11(v).

Encodings:

BibTeX
A. R. Its and V. Yu. Novokshënov (1986)
The Isomonodromic Deformation Method in the Theory of Painlevé Equations,

Lecture Notes in Mathematics, Vol. 1191, Springer-Verlag, Berlin.

External Links:

ISBN 3-540-16483-9, MathReview (Alexander A. Pankov), ZentralBlatt.

Referenced by:

§32.11(iv), §32.4(i), Alexander A. Its.

Encodings:

BibTeX
C. Itzykson and J. Drouffe (1989)
Statistical Field Theory: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems,

Vol. 2, Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-37012-4; 0-521-40806-7, MathReview (C. A. Hurst), ZentralBlatt.

Referenced by:

§23.21(iv).

Encodings:

BibTeX
C. Itzykson and J. B. Zuber (1980)
Quantum Field Theory,

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

Notes:

Reprinted by Dover, 2006.

External Links:

ISBN 0-07-032071-3, MathReview (V. E. Korepin).

Referenced by:

§22.19(ii).

Encodings:

BibTeX
A. Ivić (1985)
The Riemann Zeta-Function,

A Wiley-Interscience Publication, John Wiley & Sons Inc., New York.

Notes:

Reprinted by Dover, 2003.

External Links:

ISBN 0-471-80634-X, MathReview (S. W. Graham), ZentralBlatt.

Referenced by:

Ch.25.

Encodings:

BibTeX
K. Iwasaki, H. Kimura, S. Shimomura and M. Yoshida (1991)
From Gauss to Painlevé: A Modern Theory of Special Functions,

Aspects of Mathematics E, Vol. 16, Friedr. Vieweg & Sohn, Braunschweig, Germany.

External Links:

ISBN 3-528-06355-6, MathReview (Takeshi Sasaki), ZentralBlatt.

Referenced by:

§32.2(vi), §32.7(vii).

Encodings:

BibTeX