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11: 10.21 Zeros

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§10.21(v) Inequalities

►For bounds for the smallest real or purely imaginary zeros of $J_{\nu }\left(x\right)$ when $\nu$ is real see Ismail and Muldoon (1995). …

12: 19.8 Quadratic Transformations

… ►If , then $\rho$ is pure imaginary.

13: Bibliography M

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The characteristic numbers of the Mathieu equation with purely imaginary parameter. Phil. Mag. Series 7 8 (53), pp. 834–840.

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External Links:

Document, ZentralBlatt

Referenced by:

§28.7.

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14: 19.2 Definitions

… ►If , then $k_c$ is pure imaginary. …

15: 14.20 Conical (or Mehler) Functions

… ►For the case of purely imaginary order and argument see Dunster (2013). …

16: 2.8 Differential Equations with a Parameter

… ►For error bounds, extensions to pure imaginary or complex $u$, an extension to inhomogeneous differential equations, and examples, see Olver (1997b, Chapter 10). …

17: Bibliography B

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Asymptotic expansions of the modified Bessel function of the third kind of imaginary order. SIAM J. Appl. Math. 15, pp. 1315–1323.

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ISSN 0036-1399, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.45.

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Some Geometric Aspects of Wave Motion: Wavefront Dislocations, Diffraction Catastrophes, Diffractals. In Geometry of the Laplace Operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979), Vol. 36, pp. 13–28.

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External Links:

MathReview (I. Stewart), ZentralBlatt

Referenced by:

§36.14(i).

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Uniform asymptotic expansions of integrals with stationary point near algebraic singularity. Comm. Pure Appl. Math. 19, pp. 353–370.

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External Links:

Document, MathReview (J. G. van der Corput), ZentralBlatt

Referenced by:

§2.3(v).

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Asymptotic Expansions for the Coefficient Functions Associated with Linear Second-order Differential Equations: The Simple Pole Case. In Asymptotic and Computational Analysis (Winnipeg, MB, 1989), R. Wong (Ed.), Lecture Notes in Pure and Applied Mathematics, Vol. 124, pp. 53–73.

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External Links:

MathReview (John S. Lew), ZentralBlatt

Referenced by:

§2.8(iv).

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A Dictionary of Inequalities. Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 97, Longman, Harlow.

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ISBN 0-8493-0634-5, MathReview (Lucio Renato Berrone), ZentralBlatt

Referenced by:

§4.18, §4.5(i), §4.5(ii).

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