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11: Bibliography D

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A simplified algorithm for the second-order sound fields. J. Acoust. Soc. Amer. 108 (6), pp. 2759–2764.

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External Links:

Document

Referenced by:

§8.24(iii).

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Bessel functions $J_n(z)$ and $Y_n(z)$ of integer order and complex argument. Comput. Phys. Comm. 78 (1-2), pp. 181–189.

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Notes:

Double-precision Pascal, maximum accuracy 7D.

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ISSN 0010-4655, Document, Code, MathReview (J. P. Singhal), ZentralBlatt

Referenced by:

2nd item.

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Uniform asymptotic expansions for associated Legendre functions of large order. Proc. Roy. Soc. Edinburgh Sect. A 133 (4), pp. 807–827.

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ISSN 0308-2105, Document, MathReview, ZentralBlatt

Referenced by:

§14.15(i), §14.15(i), §14.15(ii), §14.15(ii), §14.26.

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Conical functions of purely imaginary order and argument. Proc. Roy. Soc. Edinburgh Sect. A 143 (5), pp. 929–955.

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ISSN 0308-2105, Document, Link, MathReview (Eugenia N. Petropoulou), ZentralBlatt

Referenced by:

§14.20(ix), §14.20(ix).

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A survey on orthogonal matrix polynomials satisfying second order differential equations. J. Comput. Appl. Math. 178 (1-2), pp. 169–190.

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ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§18.36(iv).

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12: 10.77 Software

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§10.77(ii) Bessel Functions–Real Argument and Integer or Half-Integer Order (including Spherical Bessel Functions)

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§10.77(iii) Bessel Functions–Real Order and Argument

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§10.77(vi) Bessel Functions–Imaginary Order and Real Argument

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§10.77(vii) Bessel Functions–Complex Order and Real Argument

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§10.77(viii) Bessel Functions–Complex Order and Argument

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13: 10.3 Graphics

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§10.3(i) Real Order and Variable

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§10.3(ii) Real Order, Complex Variable

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§10.3(iii) Imaginary Order, Real Variable

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Figure 10.3.18: ${\tilde{J}}_1\left(x\right)$, ${\tilde{Y}}_1\left(x\right)$, $0.01\le x\le 10$. Magnify

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Figure 10.3.19: ${\tilde{J}}_5\left(x\right)$, ${\tilde{Y}}_5\left(x\right)$, $0.01\le x\le 10$. Magnify

14: Bibliography L

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Inequalities and approximations for zeros of Bessel functions of small order. SIAM J. Math. Anal. 14 (2), pp. 383–388.

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ISSN 0036-1410, Document, MathReview (S. Ahmed), ZentralBlatt

Referenced by:

§10.21(iv).

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Asymptotic expansions of the Whittaker functions for large order parameter. Methods Appl. Anal. 6 (2), pp. 249–256.

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Notes:

Dedicated to Richard A. Askey on the occasion of his 65th birthday, Part II

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ISSN 1073-2772, Pdf, MathReview, ZentralBlatt

Referenced by:

§13.21(i), §13.24(ii).

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On Bessel functions of equal order and argument. Rend. Sem. Mat. Univ. Politec. Torino 50 (2), pp. 209–216 (1993).

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ISSN 0373-1243, MathReview (N. Hayek Calil), ZentralBlatt

Referenced by:

§10.14.

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Monotonicity of the differences of zeros of Bessel functions as a function of order. Proc. Amer. Math. Soc. 15 (1), pp. 91–96.

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ISSN 0002-9939, FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(ii).

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Addendum to: “Changing the order of integration”. J. Austral. Math. Soc. 14, pp. 383–384.

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Document, MathReview (G. W. Johnson), ZentralBlatt

Referenced by:

§1.5(v).

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15: 11.1 Special Notation

§11.1 Special Notation

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$x$	real variable.
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$\nu$	real or complex order.
$n$	integer order.
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16: 9.15 Mathematical Applications

… ►Airy functions play an indispensable role in the construction of uniform asymptotic expansions for contour integrals with coalescing saddle points, and for solutions of linear second-order ordinary differential equations with a simple turning point. …

17: Bibliography N

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The resurgence properties of the large order asymptotics of the Anger-Weber function I. J. Class. Anal. 4 (1), pp. 1–39.

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ISSN 1848-5979, Document, Link, MathReview (José Luis López), ZentralBlatt

Referenced by:

(11.11.10), (11.11.8), §11.11(iii).

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The resurgence properties of the large order asymptotics of the Anger-Weber function II. J. Class. Anal. 4 (2), pp. 121–147.

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External Links:

ISSN 1848-5979, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

(11.11.10), (11.11.8), §11.11(iii).

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Uniform Asymptotic Approximations of Solutions of Second-order Linear Differential Equations, with a Coalescing Simple Turning Point and Simple Pole. Ph.D. Thesis, University of Maryland, College Park, MD.

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Referenced by:

§2.8(vi).

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Diffraction Effects in Semiclassical Scattering. Montroll Memorial Lecture Series in Mathematical Physics, Cambridge University Press.

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Notes:

Also available electronically through Cambridge Books Online, ISBN 9780511599903.

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ISBN 9780521383189, Document

Referenced by:

§9.16, §9.16.

Encodings:

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18: Bibliography W

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Asymptotic expansions for second-order linear difference equations with a turning point. Numer. Math. 94 (1), pp. 147–194.

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ISSN 0029-599X, Document, MathReview (Sergey M. Zagorodnyuk), ZentralBlatt

Referenced by:

§2.9(iii).

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On the points of inflection of Bessel functions of positive order. II. Canad. J. Math. 43 (3), pp. 628–651.

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ISSN 0008-414X, MathReview (Evangelos Ifantis), ZentralBlatt

Referenced by:

§10.21(iv).

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Asymptotic expansions for second-order linear difference equations. II. Stud. Appl. Math. 87 (4), pp. 289–324.

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External Links:

ISSN 0022-2526, MathReview (Shao Zhu Chen), ZentralBlatt

Referenced by:

§2.9(ii).

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Asymptotic expansions for second-order linear difference equations. J. Comput. Appl. Math. 41 (1-2), pp. 65–94.

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External Links:

ISSN 0377-0427, Document, MathReview (Shao Zhu Chen), ZentralBlatt

Referenced by:

§2.9(i), §2.9(ii).

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Asymptotic solutions of a fourth order differential equation. Stud. Appl. Math. 118 (2), pp. 133–152.

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ISSN 0022-2526, Document, MathReview Entry

Referenced by:

§2.8(vi).

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19: 14.26 Uniform Asymptotic Expansions

§14.26 Uniform Asymptotic Expansions

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20: 10.57 Uniform Asymptotic Expansions for Large Order

§10.57 Uniform Asymptotic Expansions for Large Order

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