monotonicity properties

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1: Bibliography L

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Monotonicity properties of zeros of generalized Airy functions. Z. Angew. Math. Phys. 39 (2), pp. 267–271.

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ISSN 0044-2275, Document, MathReview (Evangelos Ifantis), ZentralBlatt

Referenced by:

§9.13(i).

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Monotonicity and convexity properties of zeros of Bessel functions. SIAM J. Math. Anal. 8 (1), pp. 171–178.

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ISSN 1095-7154, Document, MathReview (T. Erber), ZentralBlatt

Referenced by:

§10.21(iv).

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Higher monotonicity properties of certain Sturm-Liouville functions. III. Canad. J. Math. 22, pp. 1238–1265.

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ISSN 0008-414X, MathReview (G. Sansone), ZentralBlatt

Referenced by:

§10.21(ii).

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Higher monotonicity properties of certain Sturm-Liouville functions. IV. Canad. J. Math. 24, pp. 349–368.

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ISSN 0008-414X, MathReview (G. Sansone), ZentralBlatt

Referenced by:

§10.21(ii).

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Higher monotonicity properties of certain Sturm-Liouville functions.. Acta Math. 109, pp. 55–73.

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ISSN 0001-5962, Document, MathReview (G. Sansone), ZentralBlatt

Referenced by:

§10.21(ii).

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2: 10.14 Inequalities; Monotonicity

… ►For monotonicity properties of $J_{\nu }\left(\nu \right)$ and $J_{\nu }^{\prime }\left(\nu \right)$ see Lorch (1992). … ►For further monotonicity properties see Landau (1999, 2000), and Muldoon and Spigler (1984).

3: 8.3 Graphics

… ►Some monotonicity properties of ${\gamma }^{\ast }(a,x)$ and $\mathrm{\Gamma }(a,x)$ in the four quadrants of the ($a,x$)-plane in Figure 8.3.6 are given in Erdélyi et al. (1953b, §9.6). …

4: 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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5: 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). …

6: 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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7: 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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8: 3.11 Approximation Techniques

… ►They enjoy an orthogonal property with respect to integrals: …as well as an orthogonal property with respect to sums, as follows. … ►For these and further properties of Chebyshev polynomials, see Chapter 18, Gil et al. (2007a, Chapter 3), and Mason and Handscomb (2003). … ►Since $L_0=1$, $L_n$ is a monotonically increasing function of $n$, and (for example) $L_{1000}=4.07\mathrm{\dots }$, this means that in practice the gain in replacing a truncated Chebyshev-series expansion by the corresponding minimax polynomial approximation is hardly worthwhile. … ►The property …

9: 18.2 General Orthogonal Polynomials

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Kernel property

… ►For illustrations of these properties see Figures 18.4.1–18.4.7. … ►If $v(s)$ is the formal power series such that $v(u(t))=t$ then a property equivalent to (18.2.45) with $c_n=1$ is that … ►

Monotonic Weight Functions

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