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11: 10.21 Zeros

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§10.21(iv) Monotonicity Properties

… ►For further monotonicity properties see Elbert (2001), Lorch (1990, 1993, 1995), Lorch and Muldoon (2008), Lorch and Szegő (1990, 1995), and Muldoon (1981). For inequalities for zeros arising from monotonicity properties see Laforgia and Muldoon (1983). …

12: Bibliography W

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Asymptotic monotonicity of the relative extrema of Jacobi polynomials. Canad. J. Math. 46 (6), pp. 1318–1337.

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External Links:

ISSN 0008-414X, MathReview (S. I. Drobnies), ZentralBlatt

Referenced by:

§18.14(iii).

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13: Bibliography

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Monotonicity theorems and inequalities for the complete elliptic integrals. J. Comput. Appl. Math. 172 (2), pp. 289–312.

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ISSN 0377-0427, Document, MathReview (Živorad Tomovski), ZentralBlatt

Referenced by:

§19.9(i).

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14: Bibliography G

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A monotonicity property of the power function of multivariate tests. Indag. Math. (N.S.) 11 (2), pp. 209–218.

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ISSN 0019-3577, Document, MathReview (Sumitra Purkayastha), ZentralBlatt

Referenced by:

§35.9.

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15: Bibliography K

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Some completely monotonic functions of positive order. Math. Comp. 79 (271), pp. 1697–1707.

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ISSN 0025-5718, Document, FullText, MathReview (Necdet Batir), ZentralBlatt

Referenced by:

§5.6(i), §5.6(i).

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16: 22.19 Physical Applications

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Figure 22.19.1: Jacobi’s amplitude function $\mathrm{am}(x,k)$ for $0\le x\le 10\pi$ and $k=0.5,0.9999,1.0001,2$. When , $\mathrm{am}(x,k)$ increases monotonically indicating that the motion of the pendulum is unbounded in $\theta$, corresponding to free rotation about the fulcrum; compare Figure 22.16.1. … Magnify

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17: 10.17 Asymptotic Expansions for Large Argument

… ►where $𝒱$ denotes the variational operator (2.3.6), and the paths of variation are subject to the condition that $|\mathrm{\Im }t|$ changes monotonically. …

18: 10.40 Asymptotic Expansions for Large Argument

… ►where $𝒱$ denotes the variational operator (§2.3(i)), and the paths of variation are subject to the condition that $|\mathrm{\Re }t|$ changes monotonically. …

19: Bibliography B

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A monotonicity property involving ${}_{3}F_2$ and comparisons of the classical approximations of elliptical arc length. SIAM J. Math. Anal. 32 (2), pp. 403–419.

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ISSN 1095-7154, Document, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§19.9(i), §19.9(i).

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20: Bibliography M

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Higher monotonicity properties of certain Sturm-Liouville functions. V. Proc. Roy. Soc. Edinburgh Sect. A 77 (1-2), pp. 23–37.

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External Links:

MathReview (G. Sansone), ZentralBlatt

Referenced by:

§10.21(ii), (9.11.4), §9.11(iii).

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