Bibliography I
-
IEEE (2008)
IEEE Standard for Floating-Point Arithmetic.
The Institute of Electrical and Electronics Engineers, Inc..
-
IEEE (2015)
IEEE Standard for Interval Arithmetic: IEEE Std 1788-2015.
The Institute of Electrical and Electronics Engineers, Inc..
-
IEEE (2018)
IEEE Standard for Interval Arithmetic: IEEE Std 1788.1-2017.
The Institute of Electrical and Electronics Engineers, Inc..
-
IEEE (2019)
IEEE International Standard for Information Technology—Microprocessor Systems—Floating-Point arithmetic: IEEE Std 754-2019.
The Institute of Electrical and Electronics Engineers, Inc..
-
J. Igusa (1972)
Theta Functions.
Springer-Verlag, New York.
-
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 and of Bessel functions of any real order .
Linear Algebra Appl. 194, pp. 35–70.
-
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.
-
Y. Ikebe (1975)
The zeros of regular Coulomb wave functions and of their derivatives.
Math. Comp. 29, pp. 878–887.
-
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.
-
IMSL (commercial C, Fortran, and Java libraries)
Visual Numerics, Inc..
-
E. L. Ince (1926)
Ordinary Differential Equations.
Longmans, Green and Co., London.
-
E. L. Ince (1932)
Tables of the elliptic cylinder functions.
Proc. Roy. Soc. Edinburgh Sect. A 52, pp. 355–433.
-
E. L. Ince (1940a)
The periodic Lamé functions.
Proc. Roy. Soc. Edinburgh 60, pp. 47–63.
-
E. L. Ince (1940b)
Further investigations into the periodic Lamé functions.
Proc. Roy. Soc. Edinburgh 60, pp. 83–99.
-
A. E. Ingham (1932)
The Distribution of Prime Numbers.
Cambridge Tracts in Mathematics and Mathematical Physics, No.
30, Cambridge University Press, Cambridge.
-
A. E. Ingham (1933)
An integral which occurs in statistics.
Proceedings of the Cambridge Philosophical Society 29, pp. 271–276.
-
K. Inkeri (1959)
The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
-
Inverse Symbolic Calculator (website)
Centre for Experimental and Constructive Mathematics, Simon Fraser University, Canada.
-
K. Ireland and M. Rosen (1990)
A Classical Introduction to Modern Number Theory.
2nd edition, Springer-Verlag, New York.
-
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.
-
A. Iserles, S. P. Nørsett, and S. Olver (2006)
Highly Oscillatory Quadrature: The Story So Far.
In Numerical Mathematics and Advanced Applications, A. Bermudez de Castro and others (Eds.),
pp. 97–118.
-
A. Iserles (1996)
A First Course in the Numerical Analysis of Differential Equations.
Cambridge Texts in Applied Mathematics, No. 15, Cambridge University Press, Cambridge.
-
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.
-
M. E. H. Ismail and D. R. Masson (1994)
-Hermite polynomials, biorthogonal rational functions, and -beta integrals.
Trans. Amer. Math. Soc. 346 (1), pp. 63–116.
-
M. E. H. Ismail and E. Koelink (Eds.) (2005)
Theory and Applications of Special Functions.
Developments in Mathematics, Vol. 13, Springer, New York.
-
M. E. H. Ismail, D. R. Masson, and M. Rahman (Eds.) (1997)
Special Functions, -Series and Related Topics.
Fields Institute Communications, Vol. 14, American Mathematical Society, Providence, RI.
-
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.
-
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.
-
M. E. H. Ismail, M. Z. Nashed, A. I. Zayed, and A. F. Ghaleb (Eds.) (1995)
Mathematical Analysis, Wavelets, and Signal Processing.
Contemporary Mathematics, Vol. 190, American Mathematical Society, Providence, RI.
-
M. E. H. Ismail and D. W. Stanton (Eds.) (2000)
-Series from a Contemporary Perspective.
Contemporary Mathematics, Vol. 254, American Mathematical Society, Providence, RI.
-
M. E. H. Ismail (1986)
Asymptotics of the Askey-Wilson and -Jacobi polynomials.
SIAM J. Math. Anal. 17 (6), pp. 1475–1482.
-
M. E. H. Ismail (2000a)
An electrostatics model for zeros of general orthogonal polynomials.
Pacific J. Math. 193 (2), pp. 355–369.
-
M. E. H. Ismail (2000b)
More on electrostatic models for zeros of orthogonal polynomials.
Numer. Funct. Anal. Optim. 21 (1-2), pp. 191–204.
-
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.
-
M. E. H. Ismail (2009)
Classical and Quantum Orthogonal Polynomials in One Variable.
Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.
-
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.
-
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.
-
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).
-
A. R. Its and A. A. Kapaev (2003)
Quasi-linear Stokes phenomenon for the second Painlevé transcendent.
Nonlinearity 16 (1), pp. 363–386.
-
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.
-
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.
-
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.
-
C. Itzykson and J. B. Zuber (1980)
Quantum Field Theory.
International Series in Pure and Applied Physics, McGraw-Hill International Book Co., New York.
-
A. Ivić (1985)
The Riemann Zeta-Function.
A Wiley-Interscience Publication, John Wiley & Sons Inc., New York.
-
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.